Class 11 • Physics

Properties of Matter

Chapter-8

379 Questions

0 Video Solutions

109 Easy269 Medium1 Hard

Practice Questions

Click on any question to view the complete question with options and detailed solution.

Filter Questions

Difficulty

Showing 379 of 379 questions

Medium

If a small orifice is made at a height of 0.25 m from the ground, the horizontal range of water stream will be

Options:

A) 46.5 cm

B) 56.6 cm

C) 76.6 cm

D) 86.6 cm

Medium

Determine the pressure difference in tube of non-uniform cross sectional area as shown in figure. $\Delta P=?, d_1=5 \mathrm{~cm}, v_1=4 \mathrm{~m} / \mathrm{s}, d_2=2 \mathrm{~cm}, v_2=?

Options:

A) 304200 Pa

B) 304500 Pa

C) 302500 Pa

D) 303500 Pa

Medium

In an isothermal process 2 water drops of radius $1 \mathrm{~mm} are combined to form a bigger drop. Find the energy change in this process if T=0.1 \mathrm{~N} / \mathrm{m}$.

Options:

A) 1 \mu \mathrm{J}

B) 0.5 \mu \mathrm{J}

C) 0.25 \mu \mathrm{J}

D) 0.75 \mu \mathrm{J}

Medium

Assertion : Water drops take spherical shape when falling freely. Reason : Water has minimum surface tension among all liquids.

Options:

A) If both assertion and reason are true and reason is the correct explanation of assertion.

B) If both assertion and reason are true, but reason is not the correct explanation of assertion.

C) If assertion is true, but reason is false.

D) If both assertion and reason are false.

Medium

Assertion : Sometimes insects can walk on water. Reason : The gravitational force on insect is balanced by force due surface tension.

Options:

A) If both assertion and reason are true and reason is the correct explanation of assertion.

B) If both assertion and reason are true, but reason is not the correct explanation of assertion.

C) If assertion is true, but reason is false.

D) If both assertion and reason are false.

Medium

Assertion Smaller drop of water resist deformation forces better than the larger drops. Reason Excess pressure inside drop is inversely proportional to its radius.

Options:

A) Both Assertion and Reason are correct, Reason is the correct explanation of Assertion

B) Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion

C) Assertion is correct and Reason is incorrect

D) Assertion is incorrect and Reason is correct

Easy

Two wires A and B made of different materials of lengths 6.0 cm and 5.4 cm , respectively and area of cross sections 3.0 \times 10^{-5} \mathrm{~m}^2 and 4.5 \times 10^{-5} \mathrm{~m}^2, respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of A to that of B is x: 3. The value of x is \_\_\_\_

Options:

A) 2

B) 1

C) 4

D) 5

Easy

A cubical block of density \rho_b=600 \mathrm{~kg} / \mathrm{m}^3 floats in a liquid of density \rho_{\mathrm{e}}=900 \mathrm{kg} / \mathrm{m}^3. If the height of block is H=8.0 \mathrm{~cm} then height of the submerged part is \_\_\_\_ cm .

Options:

A) 6.3

B) 4.3

C) 7.3

D) 5.3

Medium

A brass wire of length 2 m and radius 1 mm at 27^{\circ} \mathrm{C} is held taut between two rigid supports. Initially it was cooled to a temperature of -43^{\circ} \mathrm{C} creating a tension T in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to 1.4 T, is \_\_\_\_ { }^{\circ} \mathrm{C}.

Options:

A) -71

B) -80

C) -65

D) -86

Easy

A small metallic sphere of diameter 2 mm and density 10.5 \mathrm{~g} / \mathrm{cm}^3 is dropped in glycerine having viscosity 10 Poise and density 1.5 \mathrm{~g} / \mathrm{cm}^3 respectively. The terminal velocity attained by the sphere is \_\_\_\_ \mathrm{cm} / \mathrm{s}. \left(\pi=\frac{22}{7}\right. and \left.g=10 \mathrm{~m} / \mathrm{s}^2\right)

Options:

A) 1.0

B) 1.5

C) 3.0

D) 2.0

Easy

The strain-stress plot for materials A, B, C and D is shown in the figure. Which material has the largest Young's modulus ?

Options:

A) B

B) A

C) D

D) C

Medium

When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises upto certain height h. If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by 1 \% each, then the height of the liquid in the tube will change by \_\_\_\_ \%.

Options:

A) +3

B) +1

C) -1

D) -3

Easy

Given below are two statements : Statement I : Pressure of a fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid. Statement II : Excess potential energy of the molecules on the surface of a liquid, when compared to interior, results in surface tension. In the light of the above statements, choose the correct answer from the options given below

Options:

A) Statement I is false but Statement II is true

B) Statement I is true but Statement II is false

C) Both Statement I and Statement II are false

D) Both Statement I and Statement II are true

Medium

Surface tension of two liquids (having same densities), T_1 and T_2, are measured using capillary rise method utilizing two tubes with inner radii of r_1 and r_2 where r_1 > r_2. The measured liquid heights in these tubes are h_1 and h_2 respectively. [Ignore the weight of the liquid above the lowest point of miniscus]. The heights h_1 and h_2 and surface tensions T_1 and T_2 satisfy the relation :

Options:

A) h_1 > h_2 and T_1 = T_2

B) h_1 < h_2 and T_1 = T_2

C) h_1 > h_2 and T_1 < T_2

D) h_1 = h_2 and T_1 = T_2

Easy

An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at 30^{\circ} \mathrm{C}. The coefficient of linear expansion of aluminium and steel are 24 \times 10^{-6} /{ }^{\circ} \mathrm{C} and 1.2 \times 10^{-5} /{ }^{\circ} \mathrm{C}, respectively. The length of this composite rod when its temperature is raised to 100^{\circ} \mathrm{C}, is \_\_\_\_ cm.

Options:

A) 120.20

B) 120.06

C) 120.15

D) 120.03

Medium

Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at A and B are 6 \mathrm{~cm}^2 and 3 \mathrm{~cm}^2 respectively. The rate of flow will be \_\_\_\_ \mathrm{cm}^3 / \mathrm{s}. (take g=10 \mathrm{~m} / \mathrm{s}^2 )

Options:

A) 100 \sqrt{3}

B) \frac{200}{\sqrt{3}}

C) 200 \sqrt{6}

D) 200 \sqrt{3}

Easy

A 3 m long wire of radius 3 mm shows an extension of 0.1 mm when loaded vertically by a mass of 50 kg in an experiment to determine Young's modulus. The value of Young's modulus of the wire as per this experiment is P \times 10^{11} \, \text{Nm}^{-2}, where the value of P is: (Take g = 3\pi \, \text{m/s}^2)

Options:

A) 2.5

B) 25

C) 10

D) 5

Medium

A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70 dyn/cm and glass water contact angle ≈ 0°) with 30° inclined with the vertical. The length of water risen in the capillary is _______ cm. (Take g = 9.8 \text{ m/s}^2)

Options:

A) \frac{82}{5}

B) \frac{68}{5}

C) \frac{57}{2}

D) \frac{71}{5}

Medium

Two wires A and B are made of same material having ratio of lengths \frac{L_A}{L_B}=\frac{1}{3} and their diameters ratio \frac{d_A}{d_B}=2. If both the wires are stretched using same force, what would be the ratio of their respective elongations?

Options:

A) 3: 4

B) 1: 12

C) 1: 3

D) 1: 6

Medium

A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of 10^5 \mathrm{~N} at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement \theta of the rod axis from its original position would be : (shear moduli, G=10^{10} \mathrm{~N} / \mathrm{m}^2 )

Options:

A) 1 / 160 \pi

B) 1 / 2 \pi

C) 1 / 4 \pi

D) 1 / 40 \pi

Medium

Two liquids A and B have \theta_A and \theta_B as contact angles in a capillary tube. If K=\cos \theta_A / \cos \theta_B, then identify the correct statement:

Options:

A) K is negative, then liquid A and liquid B have convex meniscus.

B) K is negative, then liquid A and liquid B have concave meniscus.

C) K is zero, then liquid A has convex meniscus and liquid B has concave meniscus.

D) K is negative, then liquid A has concave meniscus and liquid B has convex meniscus.

Medium

Two cylindrical vessels of equal cross sectional area of 2 \mathrm{~m}^2 contain water upto heights 10 m and 6 m , respectively. If the vessels are connected at their bottom then the work done by the force of gravity is (Density of water is 10^3 \mathrm{~kg} / \mathrm{m}^3 and \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 )

Options:

A) { }1 \times 10^5 \mathrm{~J}

B) 4 \times 10^4 \mathrm{~J}

C) 8 \times 10^4 \mathrm{~J}

D) 6 \times 10^4 \mathrm{~J}

Medium

A solid steel ball of diameter 3.6 mm acquired terminal velocity 2.45 \times 10^{-2} \mathrm{~m} / \mathrm{s} while falling under gravity through an oil of density 925 \mathrm{~kg} \mathrm{~m}^{-3}. Take density of steel as 7825 \mathrm{~kg} \mathrm{~m}^{-3} and g as 9.8 \mathrm{~m} / \mathrm{s}^2. The viscosity of the oil in SI unit is

Options:

A) 2.18

B) 1.68

C) 2.38

D) 1.99

Medium

Consider a completely full cylindrical water tank of height 1.6 m and of cross-sectional area 0.5 \mathrm{~m}^2. It has a small hole in its side at a height 90 cm from the bottom. Assume, the crosssectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is: $ \left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)

Options:

A) 2 \mathrm{~m} / \mathrm{s}

B) 5 \mathrm{~m} / \mathrm{s}

C) 3 \mathrm{~m} / \mathrm{s}

D) 4 \mathrm{~m} / \mathrm{s}

Medium

Two water drops each of radius ' r ' coalesce to form a bigger drop. If ' T ' is the surface tension, the surface energy released in this process is :

Options:

A) 4 \pi \mathrm{r}^2 \mathrm{~T}\left[2-2^{1 / 3}\right]

B) 4 \pi \mathrm{r}^2 \mathrm{~T}[1+\sqrt{2}]

C) 4 \pi \mathrm{r}^2 \mathrm{~T}\left[2-2^{2 / 3}\right]

D) 4 \pi \mathrm{r}^2 \mathrm{~T}[\sqrt{2}-1]

Easy

The fractional compression \left( \frac{\Delta V}{V} \right) of water at the depth of 2.5 km below the sea level is __________ %. Given, the Bulk modulus of water = 2 \times 10^9 N m^{-2}, density of water = 10^3 kg m^{-3}, acceleration due to gravity g = 10 m s^{-2}.

Options:

A) 1.0

B) 1.25

C) 1.75

D) 1.5

Easy

A 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water?(Given: density of water = 1000 kg m-3)

Options:

A) 400 cm3

B) 600 cm3

C) 1400 cm3

D) 4000 cm3

Medium

In the experiment for measurement of viscosity ' \eta ' of given liquid with a ball having radius R, consider following statements. A. Graph between terminal velocity V and R will be a parabola. B. The terminal velocities of different diameter balls are constant for a given liquid. C. Measurement of terminal velocity is dependent on the temperature. D. This experiment can be utilized to assess the density of a given liquid. E. If balls are dropped with some initial speed, the value of \eta will change. Choose the correct answer from the options given below:

Options:

A) C, D and E Only

B) A, B and E Only

C) A, C and D Only

D) B, D and E Only

Easy

Consider following statements: A. Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface, of a liquid. B. As the temperature of liquid rises, the coefficient of viscosity increases. C. As the temperature of gas increases, the coefficient of viscosity increases D. The onset of turbulence is determined by Reynold's number. E. In a steady flow two stream lines never intersect. Choose the correct answer from the options given below:

Options:

A) B, C, D Only

B) C, D, E Only

C) A, D, E Only

D) A, B, C Only

Medium

An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a liquid of density 1000 \mathrm{~kg} / \mathrm{m}^3. If the pressure inside the bubble is 2100 \mathrm{~N} / \mathrm{m}^2 greater than the atmospheric pressure, then the surface tension of the liquid in SI unit is (use g=10 \mathrm{~m} / \mathrm{s}^2 )

Options:

A) 0.02

B) 0.05

C) 0.25

D) 0.1

Medium

The amount of work done to break a big water drop of radius ' R ' into 27 small drops of equal radius is 10 J . The work done required to break the same big drop into 64 small drops of equal radius will be

Options:

A) 20 J

B) 10 J

C) 5 J

D) 15 J

Easy

A massless spring gets elongated by amount x_1 under a tension of 5 N . Its elongation is x_2 under the tension of 7 N . For the elongation of \left(5 x_1-2 x_2\right), the tension in the spring will be,

Options:

A) 20 N

B) 39 N

C) 11 N

D) 15 N

Easy

Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is P_1. The reading of the pressure gauge falls to P_2 when the valve is opened. The speed of water flowing in the pipe is proportional to

Options:

A) \left(P_1-P_2\right)^2

B) \sqrt{\mathrm{P}_1-\mathrm{P}_2}

C) P_1-P_2

D) \left(P_1-P_2\right)^4

Easy

Given below are two statements: Statement I: The hot water flows faster than cold water Statement II: Soap water has higher surface tension as compared to fresh water. In the light above statements, choose the correct answer from the options given below

Options:

A) Both Statement I and Statement II are false

B) Both Statement I and Statement II are true

C) Statement I is false but Statement II is true

D) Statement I is true but Statement II is false

Easy

A tube of length L is shown in the figure. The radius of cross section at the point (1) is 2 cm and at the point (2) is 1 cm , respectively. If the velocity of water entering at point (1) is 2 \mathrm{~m} / \mathrm{s}, then velocity of water leaving the point (2) will be

Options:

A) 4 m/s

B) 6 m/s

C) 2 m/s

D) 8 m/s

Easy

A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider g as acceleration due to gravity)

Options:

A) 2 Mg

B) \frac{3}{2} \mathrm{Mg}

C) \frac{\mathrm{Mg}}{2}

D) Mg

Easy

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:

Options:

A) 1: 9

B) 1: 27

C) 1: 81

D) 1: 3

Medium

A spherical ball of radius $1 \times 10^{-4} \mathrm{~m} and density 10^5 \mathrm{~kg} / \mathrm{m}^3 falls freely under gravity through a distance h before entering a tank of water, If after entering in water the velocity of the ball does not change, then the value of h is approximately: (The coefficient of viscosity of water is 9.8 \times 10^{-6} \mathrm{~N} \mathrm{~s} / \mathrm{m}^2$)

Options:

A) 2518 m

B) 2396 m

C) 2249 m

D) 2296 m

Medium

A sphere of relative density $\sigma and diameter D has concentric cavity of diameter d. The ratio of \frac{D}{d}$, if it just floats on water in a tank is :

Options:

A) \left(\frac{\sigma-2}{\sigma+2}\right)^{1 / 3}

B) \left(\frac{\sigma+1}{\sigma-1}\right)^{1 / 3}

C) \left(\frac{\sigma-1}{\sigma}\right)^{1 / 3}

D) \left(\frac{\sigma}{\sigma-1}\right)^{1 / 3}

Medium

A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil (specific gravity of Kerosene oil = 0.8, specific gravity of ice = 0.9):

Options:

A) 5 : 4

B) 9 : 10

C) 8 : 9

D) 1 : 1

Medium

Young's modulus is determined by the equation given by $\mathrm{Y}=49000 \frac{\mathrm{m}}{\mathrm{l}} \frac{\mathrm{dyne}}{\mathrm{cm}^2} where M is the mass and l is the extension of wire used in the experiment. Now error in Young modules (Y) is estimated by taking data from M-l plot in graph paper. The smallest scale divisions are 5 \mathrm{~g} and 0.02 \mathrm{~cm} along load axis and extension axis respectively. If the value of M and l are 500 \mathrm{~g} and 2 \mathrm{~cm} respectively then percentage error of Y$ is :

Options:

A) 2%

B) 0.02%

C) 0.5%

D) 0.2%

Easy

Correct Bernoulli's equation is (symbols have their usual meaning) :

Options:

A) P+\frac{1}{2} \rho g h+\frac{1}{2} \rho v^2=$ constant

B) P+m g h+\frac{1}{2} m v^2=$ constant

C) P+\rho g h+\rho v^2=$ constant

D) P+\rho g h+\frac{1}{2} \rho v^2=$ constant

Easy

Pressure inside a soap bubble is greater than the pressure outside by an amount : (given : $\mathrm{R}= Radius of bubble, \mathrm{S}=$ Surface tension of bubble)

Options:

A) \frac{S}{R}

B) \frac{4 \mathrm{~S}}{\mathrm{R}}

C) \frac{4 \mathrm{R}}{\mathrm{S}}

D) \frac{2 S}{R}

Easy

A small ball of mass $m and density \rho is dropped in a viscous liquid of density \rho_0$. After sometime, the ball falls with constant velocity. The viscous force on the ball is :

Options:

A) m g\left(1-\frac{\rho_0}{\rho}\right)

B) m g\left(\frac{\rho_0}{\rho}-1\right)

C) m g\left(1-\rho \rho_0\right)

D) m g\left(1+\frac{\rho}{\rho_0}\right)

Easy

Match List I with List II : LIST I LIST II A. A force that restores an elastic body of unit area to its original state I. Bulk modulus B. Two equal and opposite forces parallel to opposite faces II. Young's modulus C. Forces perpendicular everywhere to the surface per unit area same everywhere III. Stress D. Two equal and opposite forces perpendicular to opposite faces Choose the correct answer from the options given below : IV. Shear modulus Choose the correct answer from the options given below :

Options:

A) (A)-(IV), (B)-(II), (C)-(III), (D)-(I)

B) (A)-(III), (B)-(IV), (C)-(I), (D)-(II)

C) (A)-(II), (B)-(IV), (C)-(I), (D)-(III)

D) (A)-(III), (B)-(I), (C)-(II), (D)-(IV)

Medium

Given below are two statements : Statement I : When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary. The contact angle may be $0^{\circ}$. Statement II : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well. In the light of the above statement, choose the correct answer from the options given below.

Options:

A) Statement I is true and Statement II is false

B) Statement I is false but Statement II is true

C) Both Statement I and Statement II are true

D) Both Statement I and Statement II are false

Medium

Given below are two statements : Statement I : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well. Statement II : The rise of a liquid in a capillary tube does not depend on the inner radius of the tube. In the light of the above statements, choose the correct answer from the options given below :

Options:

A) Both Statement I and Statement II are false.

B) Both Statement I and Statement II are true.

C) Statement I is false but Statement II is true.

D) Statement I is true but Statement II is false.

Easy

Given below are two statements : Statement I : When speed of liquid is zero everywhere, pressure difference at any two points depends on equation $\mathrm{P}_1-\mathrm{P}_2=\rho g\left(\mathrm{~h}_2-\mathrm{h}_1\right). Statement II : In ventury tube shown 2 \mathrm{gh}=v_1^2-v_2^2$ In the light of the above statements, choose the most appropriate answer from the options given below.

Options:

A) Statement I is correct but Statement II is incorrect.

B) Both Statement I and Statement II are correct.

C) Both Statement I and Statement II are incorrect.

D) Statement I is incorrect but Statement II is correct.

Medium

A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become :

Options:

A) \frac{1}{100} th

B) \frac{1}{10} th

C) 100 times

D) 10 times

Easy

With rise in temperature, the Young's modulus of elasticity :

Options:

A) changes erratically

B) increases

C) decreases

D) remains unchanged

Medium

A small spherical ball of radius $r, falling through a viscous medium of negligible density has terminal velocity 'v'. Another ball of the same mass but of radius 2 r$, falling through the same viscous medium will have terminal velocity:

Options:

A) 4 \mathrm{v}

B) 2 \mathrm{~V}

C) \frac{v}{4}

D) \frac{\mathrm{v}}{2}

Medium

A small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct representation of the velocity time graph for the transit of the ball?

Options:

Easy

Young's modules of material of a wire of length '$L' and cross-sectional area A is Y$. If the length of the wire is doubled and cross-sectional area is halved then Young's modules will be :

Options:

A) 4 Y

B) 2 Y

C) \mathrm{\frac{Y}{4}}

D) Y

Medium

A small liquid drop of radius $R is divided into 27 identical liquid drops. If the surface tension is T$, then the work done in the process will be:

Options:

A) 4 \pi \mathrm{R}^2 \mathrm{~T}

B) 8 \pi R^2 \mathrm{~T}

C) \frac{1}{8} \pi R^2 T

D) 3 \pi R^2 \mathrm{~T}

Easy

A wire of length $L and radius r is clamped at one end. If its other end is pulled by a force F, its length increases by l$. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become:

Options:

A) 2 times

B) 4 times

C) 3 times

D) \frac{3}{2}$ times

Easy

Given below are two statements: Statement I : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water. Statement II : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in cold water. In the light of the above statements, choose the most appropriate from the options given below

Options:

A) Both Statement I and Statement II are false

B) Both Statement I and Statement II are true

C) Statement I is true but Statement II is false

D) Statement I is false but Statement II is true

Easy

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The property of body, by virtue of which it tends to regain its original shape when the external force is removed, is Elasticity. Reason (R) : The restoring force depends upon the bonded inter atomic and inter molecular force of solid. In the light of the above statements, choose the correct answer from the options given below :

Options:

A) (A) is false but (R) is true

B) Both (A) and (R) are true but (R) is not the correct explanation of (A)

C) Both (A) and (R) are true and (R) is the correct explanation of (A)

D) (A) is true but (R) is false

Easy

Given below are two statements : Statement (I) :Viscosity of gases is greater than that of liquids. Statement (II) : Surface tension of a liquid decreases due to the presence of insoluble impurities. In the light of the above statements, choose the most appropriate answer from the options given below :

Options:

A) Statement I is correct but statement II is incorrect

B) Statement I is incorrect but Statement II is correct

C) Both Statement I and Statement II are incorrect

D) Both Statement I and Statement II are correct

Easy

A wire of length ' L ' and radius ' r ' is clamped rigidly at one end. When the other end of the wire is pulled by a force f, its length increases by ' l '. Another wire of same material of length ' 2 \mathrm{~L} ' and radius ' 2 r ' is pulled by a force ' 2 f '. Then the increase in its length will be :

Options:

A) 2 l

B) 4 l

C) l

D) l / 2

Medium

Given below are two statements: one is labelled as Assertion $\mathbf{A} and the other is labelled as Reason \mathbf{R} Assertion A : A spherical body of radius (5 \pm 0.1) \mathrm{mm} having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is 4 \%$. Reason R : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius. In the light of the above statements, choose the correct answer from the options given below

Options:

A) A is false but $\mathbf{R}$ is true

B) \mathrm{A} is true but \mathbf{R}$ is false

C) Both $\mathbf{A} and \mathbf{R} are true but \mathbf{R} is NOT the correct explanation of \mathbf{A}

D) Both $\mathbf{A} and \mathbf{R} are true and \mathbf{R} is the correct explanation of \mathbf{A}

Easy

The figure shows a liquid of given density flowing steadily in horizontal tube of varying cross - section. Cross sectional areas at $\mathrm{A} is 1.5 \mathrm{~cm}^{2}, and \mathrm{B} is 25 \mathrm{~mm}^{2}, if the speed of liquid at \mathrm{B} is 60 \mathrm{~cm} / \mathrm{s} then \left(\mathrm{P}_{\mathrm{A}}-\mathrm{P}_{\mathrm{B}}\right) is : (Given \mathrm{P}_{\mathrm{A}} and \mathrm{P}_{\mathrm{B}} are liquid pressures at \mathrm{A} and \mathrm{B}% points. density \rho=1000 \mathrm{~kg} \mathrm{~m}^{-3} \mathrm{A} and \mathrm{B}$ are on the axis of tube

Options:

A) 27 \mathrm{~Pa}

B) 175 \mathrm{~Pa}

C) 135 \mathrm{~Pa}

D) 36 \mathrm{~Pa}

Medium

Under isothermal condition, the pressure of a gas is given by $\mathrm{P}=a \mathrm{~V}^{-3}, where a is a constant and \mathrm{V}$ is the volume of the gas. The bulk modulus at constant temperature is equal to

Options:

A) \frac{P}{2}

B) 2 P

C) 3 P

D) P

Easy

A body cools from $80^{\circ} \mathrm{C} to 60^{\circ} \mathrm{C} in 5 minutes. The temperature of the surrounding is 20^{\circ} \mathrm{C}. The time it takes to cool from 60^{\circ} \mathrm{C} to 40^{\circ} \mathrm{C}$ is :

Options:

A) 500 s

B) \frac{25}{3} \mathrm{~S}

C) 450 s

D) 420 s

Medium

Eight equal drops of water are falling through air with a steady speed of $10 \mathrm{~cm} / \mathrm{s}$. If the drops coalesce, the new velocity is:-

Options:

A) 40 \mathrm{~cm} / \mathrm{s}

B) 16 \mathrm{~cm} / \mathrm{s}

C) 10 \mathrm{~cm} / \mathrm{s}

D) 5 \mathrm{~cm} / \mathrm{s}

Medium

Young's moduli of the material of wires A and B are in the ratio of $1: 4, while its area of cross sections are in the ratio of 1: 3. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires \mathrm{A} and \mathrm{B}$ will be in the ratio of [Assume length of wires A and B are same]

Options:

A) 1 : 12

B) 1 : 36

C) 12 : 1

D) 36 : 1

Easy

Given below are two statements: Statement I : Pressure in a reservoir of water is same at all points at the same level of water. Statement II : The pressure applied to enclosed water is transmitted in all directions equally. In the light of the above statements, choose the correct answer from the options given below:

Options:

A) Both Statement I and Statement II are false

B) Statement I is false but Statement II is true

C) Statement I is true but Statement II is false

D) Both Statement I and Statement II are true

Easy

A hydraulic automobile lift is designed to lift vehicles of mass $5000 \mathrm{~kg}. The area of cross section of the cylinder carrying the load is 250 \mathrm{~cm}^{2}. The maximum pressure the smaller piston would have to bear is \left[\right. Assume \left.g=10 \mathrm{~m} / \mathrm{s}^{2}\right]

Options:

A) 20 \times 10^{+6} \mathrm{~Pa}

B) 200 \times 10^{+6} \mathrm{~Pa}

C) 2 \times 10^{+5} \mathrm{~Pa}

D) 2 \times 10^{+6} \mathrm{~Pa}

Medium

An air bubble of volume $1 \mathrm{~cm}^{3} rises from the bottom of a lake 40 \mathrm{~m} deep to the surface at a temperature of 12^{\circ} \mathrm{C}. The atmospheric pressure is 1 \times 10^{5} \mathrm{~Pa} the density of water is 1000 \mathrm{~kg} / \mathrm{m}^{3} and \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}. There is no difference of the temperature of water at the depth of 40 \mathrm{~m}$ and on the surface. The volume of air bubble when it reaches the surface will be:

Options:

A) 4 \mathrm{~cm}^{3}

B) 3 \mathrm{~cm}^{3}

C) 2 \mathrm{~cm}^{3}

D) 5 \mathrm{~cm}^{3}

Easy

An aluminium rod with Young's modulus $Y=7.0 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2} undergoes elastic strain of 0.04 \%$. The energy per unit volume stored in the rod in SI unit is:

Options:

A) 5600

B) 2800

C) 11200

D) 8400

Easy

Given below are two statements: one is labelled as Assertion $\mathbf{A} and the other is labelled as Reason \mathbf{R}$ Assertion A: When you squeeze one end of a tube to get toothpaste out from the other end, Pascal's principle is observed. Reason R: A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its container. In the light of the above statements, choose the most appropriate answer from the options given below

Options:

A) Both A and R are correct but R is NOT the correct explanation of A

B) A is not correct but R is correct

C) A is correct but R is not correct

D) Both A and B are correct and R is the correct explanation of A

Easy

A small ball of mass $\mathrm{M} and density \rho is dropped in a viscous liquid of density \rho_{0}$. After some time, the ball falls with a constant velocity. What is the viscous force on the ball ?

Options:

A) \mathrm{F}=\mathrm{Mg}\left(1-\frac{\rho_{\mathrm{O}}}{\rho}\right)

B) \mathrm{F}=\mathrm{Mg}\left(1+\frac{\rho}{P_{o}}\right)

C) \mathrm{F}=\mathrm{Mg}\left(1+\frac{\rho_{\mathrm{o}}}{\rho}\right)

D) F=M g\left(1 \pm \rho \rho_{0}\right)

Easy

The Young's modulus of a steel wire of length $6 \mathrm{~m} and cross-sectional area 3 \mathrm{~mm}^{2}, is 2 \times 10^{11}~\mathrm{N} / \mathrm{m}^{2}. The wire is suspended from its support on a given planet. A block of mass 4 \mathrm{~kg} is attached to the free end of the wire. The acceleration due to gravity on the planet is \frac{1}{4} of its value on the earth. The elongation of wire is (Take g on the earth =10 \mathrm{~m} / \mathrm{s}^{2}$) :

Options:

A) 0.1 cm

B) 1 cm

C) 0.1 mm

D) 1 mm

Medium

A mercury drop of radius $10^{-3}~\mathrm{m} is broken into 125 equal size droplets. Surface tension of mercury is 0.45~\mathrm{Nm}^{-1}$. The gain in surface energy is :

Options:

A) 28\times10^{-5}~\mathrm{J}

B) 17.5\times10^{-5}~\mathrm{J}

C) 5\times10^{-5}~\mathrm{J}

D) 2.26\times10^{-5}~\mathrm{J}

Easy

For a solid rod, the Young's modulus of elasticity is 3.2 \times 10^{11} \mathrm{Nm}^{-2} and density is 8 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}. The velocity of longitudinal wave in the rod will be.

Options:

A) 3.65 \times 10^3 \mathrm{~ms}^{-1}

B) 6.32 \times 10^3 \mathrm{~ms}^{-1}

C) 18.96 \times 10^3 \mathrm{~ms}^{-1}

D) 145.75 \times 10^3 \mathrm{~ms}^{-1}

Easy

Under the same load, wire A having length 5.0 \mathrm{~m} and cross section 2.5 \times 10^{-5} \mathrm{~m}^{2} stretches uniformly by the same amount as another wire B of length 6.0 \mathrm{~m} and a cross section of 3.0 \times 10^{-5} \mathrm{m}^{2} stretches. The ratio of the Young's modulus of wire A to that of wire B will be :

Options:

A) 1: 2

B) 1: 4

C) 1: 1

D) 1: 10

Medium

If 1000 droplets of water of surface tension $0.07 \mathrm{~N} / \mathrm{m}, having same radius 1 \mathrm{~mm} each, combine to from a single drop. In the process the released surface energy is :- \left( {\mathrm{Take}\,\pi = {{22} \over 7}} \right)

Options:

A) 7 .92 \times 10^{-4} \mathrm{~J}

B) 7 .92 \times 10^{-6} \mathrm{~J}

C) 8 .8 \times 10^{-5} \mathrm{~J}

D) 9 .68 \times 10^{-4} \mathrm{~J}

Easy

A force is applied to a steel wire 'A', rigidly clamped at one end. As a result elongation in the wire is 0.2 \mathrm{~mm}. If same force is applied to another steel wire ' \mathrm{B} ' of double the length and a diameter 2.4 times that of the wire ' \mathrm{A} ', the elongation in the wire ' \mathrm{B} ' will be (wires having uniform circular cross sections)

Options:

A) 6 .9 \times 10^{-2} \mathrm{~mm}

B) 6.06 \times 10^{-2} \mathrm{~mm}

C) 2.77 \times 10^{-2} \mathrm{~mm}

D) 3.0 \times 10^{-2} \mathrm{~mm}

Easy

The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, $5 \mathrm{~cm}. If the tube is dipped in a similar manner in another liquid \mathrm{B} of surface tension and density double the values of liquid \mathrm{A}, the height of liquid column raised in liquid \mathrm{B}$ would be __________ m.

Options:

A) 0.05

B) 0.20

C) 0.5

D) 0.10

Medium

Choose the correct relationship between Poisson ratio $(\sigma), bulk modulus (K) and modulus of rigidity (\eta)$ of a given solid object :

Options:

A) \sigma=\frac{3 K+2 \eta}{6 K+2 \eta}

B) \sigma=\frac{3 K-2 \eta}{6 K+2 \eta}

C) \sigma=\frac{6 K+2 \eta}{3 K-2 \eta}

D) \sigma=\frac{6 K-2 \eta}{3 K-2 \eta}

Medium

A fully loaded boeing aircraft has a mass of $5.4\times10^5 kg. Its total wing area is 500 m^2. It is in level flight with a speed of 1080 km/h. If the density of air \rho is 1.2 kg m^{-3}, the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be. (\mathrm{g=10~m/s^2}$)

Options:

A) 16

B) 8

C) 6

D) 10

Easy

Surface tension of a soap bubble is $2.0 \times 10^{-2} \mathrm{Nm}^{-1}. Work done to increase the radius of soap bubble from 3.5 \mathrm{~cm} to 7 \mathrm{~cm} will be: Take \left[\pi=\frac{22}{7}\right]

Options:

A) 18 .48 \times 10^{-4} \mathrm{~J}

B) 5.76 \times 10^{-4} \mathrm{~J}

C) 0.72 \times 10^{-4} \mathrm{~J}

D) 9.24 \times 10^{-4} \mathrm{~J}

Easy

A bicycle tyre is filled with air having pressure of $270 ~\mathrm{kPa} at 27^{\circ} \mathrm{C}. The approximate pressure of the air in the tyre when the temperature increases to 36^{\circ} \mathrm{C}$ is

Options:

A) 262 kPa

B) 360 kPa

C) 270 kPa

D) 278 kPa

Easy

Match List I with List II List I List II A. Surface tension I. $\mathrm{kg~m^{-1}~s^{-1}} B. Pressure II. \mathrm{kg~ms^{-1}} C. Viscosity III. \mathrm{kg~m^{-1}~s^{-2}} D. Impulse IV. \mathrm{kg~s^{-2}}$ Choose the correct answer from the options given below :

Options:

A) A-IV, B-III, C-I, D-II

B) A-IV, B-III, C-II, D-I

C) A-I, B-I, C-III, D-IV

D) A-III, B-IV, C-I, D-II

Easy

A bowl filled with very hot soup cools from 98$^\circC to 86^\circC in 2 minutes when the room temperature is 22^\circC. How long it will take to cool from 75^\circC to 69^\circ$C?

Options:

A) 2 minutes

B) 0.5 minute

C) 1.4 minutes

D) 1 minute

Easy

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : Steel is used in the construction of buildings and bridges. Reason R : Steel is more elastic and its elastic limit is high. In the light of above statements, choose the most appropriate answer from the options given below

Options:

A) Both A and R are correct and R is the correct explanation of A

B) A is correct but R is not correct

C) Both A and R are correct but R is NOT the correct explanation of A

D) A is not correct but R is correct

Medium

The frequency ($\nu) of an oscillating liquid drop may depend upon radius (r) of the drop, density (\rho) of liquid and the surface tension (s) of the liquid as \nu=r^a\rho^b s^c$. The values of a, b and c respectively are

Options:

A) \left( {{3 \over 2},{1 \over 2}, - {1 \over 2}} \right)

B) \left( { - {3 \over 2}, - {1 \over 2},{1 \over 2}} \right)

C) \left( {{3 \over 2}, - {1 \over 2},{1 \over 2}} \right)

D) \left( { - {3 \over 2},{1 \over 2},{1 \over 2}} \right)

Easy

A 100 m long wire having cross-sectional area $\mathrm{6.25\times10^{-4}~m^2} and Young's modulus is \mathrm{10^{10}~Nm^{-2}}$ is subjected to a load of 250 N, then the elongation in the wire will be :

Options:

A) \mathrm{6.25\times10^{-6}~m}

B) \mathrm{4\times10^{-3}~m}

C) \mathrm{4\times10^{-4}~m}

D) \mathrm{6.25\times10^{-3}~m}

Easy

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Clothes containing oil or grease stains cannot be cleaned by water wash. Reason (R): Because the angle of contact between the oil/grease and water is obtuse. In the light of the above statements, choose the correct answer from the option given below.

Options:

A) Both (A) and (R) are true and (R) is the correct explanation of (A)

B) Both (A) and (R) are true but (R) is not the correct explanation of (A)

C) (A) is true but (R) is false

D) (A) is false but (R) is true

Easy

If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modulus of the material of the wire will :

Options:

A) remain same

B) become 8 times its initial value

C) become $\frac{1}{4}$ of its initial value

D) become 4 times its initial value

Easy

A pressure-pump has a horizontal tube of cross sectional area $10 \mathrm{~cm}^{2} for the outflow of water at a speed of 20 \mathrm{~m} / \mathrm{s}. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is : [given: density of water =1000 \mathrm{~kg} / \mathrm{m}^{3}$]

Options:

A) 300 N

B) 500 N

C) 250 N

D) 400 N

Medium

Consider a cylindrical tank of radius $1 \mathrm{~m} is filled with water. The top surface of water is at 15 \mathrm{~m} from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of 5 \mathrm{~m} from the bottom. A force of 5 \times 10^{5} \mathrm{~N} is applied an the top surface of water using a piston. The speed of ifflux from the hole will be : (given atmospheric pressure \mathrm{P}_{\mathrm{A}}=1.01 \times 10^{5} \mathrm{~Pa}, density of water \rho_{\mathrm{W}}=1000 \mathrm{~kg} / \mathrm{m}^{3} and gravitational acceleration \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ )

Options:

A) 11.6 m/s

B) 10.8 m/s

C) 17.8 m/s

D) 14.4 m/s

Easy

A balloon has mass of $10 \mathrm{~g} in air. The air escapes from the balloon at a uniform rate with velocity 4.5 \mathrm{~cm} / \mathrm{s}. If the balloon shrinks in 5 \mathrm{~s}$ completely. Then, the average force acting on that balloon will be (in dyne).

Options:

A) 3

B) 9

C) 12

D) 18

Easy

The force required to stretch a wire of cross-section $1 \mathrm{~cm}^{2} to double its length will be : (Given Yong's modulus of the wire =2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$)

Options:

A) 1 \times 10^{7} \mathrm{~N}

B) 1.5 \times 10^{7} \mathrm{~N}

C) 2 \times 10^{7} \mathrm{~N}

D) 2.5 \times 10^{7} \mathrm{~N}

Easy

A steel wire of length $3.2 \mathrm{~m}\left(\mathrm{Y}_{\mathrm{s}}=2.0 \times 10^{11} \,\mathrm{Nm}^{-2}\right) and a copper wire of length 4.4 \mathrm{~m}\left(\mathrm{Y}_{\mathrm{c}}=1.1 \times 10^{11} \,\mathrm{Nm}^{-2}\right), both of radius 1.4 \mathrm{~mm} are connected end to end. When stretched by a load, the net elongation is found to be 1.4 \mathrm{~mm}. The load applied, in Newton, will be: \quad\left(\right. Given \pi=\frac{22}{7}$)

Options:

A) 360

B) 180

C) 1080

D) 154

Medium

Two cylindrical vessels of equal cross-sectional area $16 \mathrm{~cm}^{2} contain water upto heights 100 \mathrm{~cm} and 150 \mathrm{~cm} respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is [Take, density of water =10^{3} \mathrm{~kg} / \mathrm{m}^{3} and \mathrm{g}=10 \mathrm{~ms}^{-2}$ ] :

Options:

A) 0.25 J

B) 1 J

C) 8 J

D) 12 J

Easy

The area of cross section of the rope used to lift a load by a crane is $2.5 \times 10^{-4} \mathrm{~m}^{2}. The maximum lifting capacity of the crane is 10 metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross section of the rope should be : (take g=10 \,m s^{-2}$ )

Options:

A) 6.25\times 10^{-4} \mathrm{~m}^{2}

B) 10\times 10^{-4} \mathrm{~m}^{2}

C) 1\times 10^{-4} \mathrm{~m}^{2}

D) 1.67\times 10^{-4} \mathrm{~m}^{2}

Medium

A water drop of radius $1 \mathrm{~cm} is broken into 729 equal droplets. If surface tension of water is 75 dyne/ \mathrm{cm}, then the gain in surface energy upto first decimal place will be : (Given \pi=3.14$ )

Options:

A) 8.5 \times 10^{-4} \mathrm{~J}

B) 8.2 \times 10^{-4} \mathrm{~J}

C) 7.5 \times 10^{-4} \mathrm{~J}

D) 5.3 \times 10^{-4} \mathrm{~J}

Medium

A drop of liquid of density $\rho is floating half immersed in a liquid of density {\sigma} and surface tension 7.5 \times 10^{-4} Ncm-1. The radius of drop in \mathrm{cm} will be : (g = 10 ms-$2)

Options:

A) \frac{15}{\sqrt{(2 \rho-\sigma)}}

B) \frac{15}{\sqrt{(\rho-\sigma)}}

C) \frac{3}{2 \sqrt{(\rho-\sigma)}}

D) \frac{3}{20 \sqrt{(2 \rho-\sigma)}}

Medium

An air bubble of negligible weight having radius r rises steadily through a solution of density $\sigma$ at speed v. The coefficient of viscosity of the solution is given by :

Options:

A) \eta = {{4r\sigma g} \over {9v}}

B) \eta = {{2{r^2}\sigma g} \over {9v}}

C) \eta = {{2\pi {r^2}\sigma g} \over {9v}}

D) \eta = {{2{r^2}\sigma g} \over {3\pi v}}

100

Medium

A wire of length L is hanging from a fixed support. The length changes to L1 and L2 when masses 1 kg and 2 kg are suspended respectively from its free end. Then the value of L is equal to :

Options:

A) \sqrt {{L_1}{L_2}}

B) {{{L_1} + {L_2}} \over 2}

C) 2{L_1} - {L_2}

D) 3{L_1} - 2{L_2}

101

Medium

A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of 1 kgs$-1 and at a speed of 10 ms-1. Then, the initial acceleration of the block, in ms-$2, will be :

Options:

A) 3

B) 6

C) 5

D) 4

102

Easy

A water drop of radius 1 $\mum falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is 1.8 \times 10-5 Nsm-2 and its density is negligible as compared to that of water 106 gm-3. Terminal velocity of the water drop is : (Take acceleration due to gravity = 10 ms-$2)

Options:

A) 145.4 $\times 10-6 ms-$1

B) 118.0 $\times 10-6 ms-$1

C) 132.6 $\times 10-6 ms-$1

D) 123.4 $\times 10-6 ms-$1

103

Easy

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Product of Pressure (P) and time (t) has the same dimension as that of coefficient of viscosity. Reason R : Coefficient of viscosity = ${{Force} \over {Velocity\,gradient}}$ Choose the correct answer from the options given below :

Options:

A) Both A and R are true, and R is the correct explanation of A.

B) Both A and R are true but R is NOT the correct explanation of A.

C) A is true but R is false.

D) A is false but R is true.

104

Medium

A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0.075 N/m. In this process the gain in surface energy will be :

Options:

A) 2.8 $\times 10-$4 J

B) 1.5 $\times 10-$3 J

C) 1.9 $\times 10-$4 J

D) 9.4 $\times 10-$5 J

105

Easy

When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v. It reaches the bottom of the lake 4.0 s after it is dropped. The approximate depth of the lake is :

Options:

A) 19.6 m

B) 29.4 m

C) 39.2 m

D) 73.5 m

106

Easy

The velocity of a small ball of mass 'm' and density d1, when dropped in a container filled with glycerin, becomes constant after some time. If the density of glycerin is d2, then the viscous force acting on the ball, will be :

Options:

A) mg\left( {1 - {{{d_1}} \over {{d_2}}}} \right)

B) mg\left( {1 - {{{d_2}} \over {{d_1}}}} \right)

C) mg\left( {{{{d_1}} \over {{d_2}}} - 1} \right)

D) mg\left( {{{{d_2}} \over {{d_1}}} - 1} \right)

107

Easy

If p is the density and $\eta$ is coefficient of viscosity of fluid which flows with a speed v in the pipe of diameter d, the correct formula for Reynolds number Re is :

Options:

A) {R_e} = {{\eta d} \over {\rho v}}

B) {R_e} = {{\rho v} \over {\eta d}}

C) {R_e} = {{\rho vd} \over \eta }

D) {R_e} = {\eta \over {\rho vd}}

108

Easy

The terminal velocity (vt) of the spherical rain drop depends on the radius (r) of the spherical rain drop as :

Options:

A) r1/2

B) r

C) r2

D) r3

109

Easy

Potential energy as a function of r is given by $U = {A \over {{r^{10}}}} - {B \over {{r^5}}}$, where r is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be :

Options:

A) {\left( {{A \over B}} \right)^{{1 \over 5}}}

B) {\left( {{B \over A}} \right)^{{1 \over 5}}}

C) {\left( {{2A \over B}} \right)^{{1 \over 5}}}

D) {\left( {{B \over 2A}} \right)^{{1 \over 5}}}

110

Easy

The bulk modulus of a liquid is 3 $\times 1010 Nm-$2. The pressure required to reduce the volume of liquid by 2% is :

Options:

A) 3 $\times 108 Nm-$2

B) 9 $\times 108 Nm-$2

C) 6 $\times 108 Nm-$2

D) 12 $\times 108 Nm-$2

111

Easy

Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 $\times 103 kg. The inner and outer radii of each column are 50 cm and 100 cm respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use Y = 2.0 \times$ 1011 Pa, g = 9.8 m/s2]

Options:

A) 3.60 $\times 10-$8

B) 2.60 $\times 10-$7

C) 1.87 $\times 10-$3

D) 7.07 $\times 10-$4

112

Easy

A uniform heavy rod of weight 10 kg ms$-2, cross-sectional area 100 cm2 and length 20 cm is hanging from a fixed support. Young modulus of the material of the rod is 2 \times 1011 Nm-$2. Neglecting the lateral contraction, find the elongation of rod due to its own weight.

Options:

A) 2 $\times 10-$9 m

B) 5 $\times 10-$8 m

C) 4 $\times 10-$8 m

D) 5 $\times 10-$10 m

113

Easy

In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius 2.0 $\times 10-5 m and density 1.2 \times 103 kgm-3 ? Take viscosity of liquid = 1.8 \times 10-5 Nsm-$2. (Neglect buoyancy due to air).

Options:

A) 3.8 $\times 10-$11 N

B) 3.9 $\times 10-$10 N

C) 1.8 $\times 10-$10 N

D) 5.8 $\times 10-$10 N

114

Medium

Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is ${{24} \over \pi } \times {10^2}$ Nm-2. What is the minimum radius of the wire ? (Take g = 10 ms-2)

Options:

A) 125 cm

B) 1250 cm

C) 12.5 cm

D) 1.25 cm

115

Medium

Two narrow bores of diameter 5.0 mm and 8.0 mm are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of two limbs of the tube. [Take surface tension of water T = 7.3 $\times 10-2 Nm-1, angle of contact = 0, g = 10 ms2 and density of water = 1.0 \times 103 kg m-$3]

Options:

A) 3.62 mm

B) 2.19 mm

C) 5.34 mm

D) 4.97 mm

116

Medium

A raindrop with radius R = 0.2 mm falls from a cloud at a height h = 2000 m above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attained by the raindrop is :[Density of water fw = 1000 kg m$-3 and Density of air fa = 1.2 kg m-3, g = 10 m/s2, Coefficient of viscosity of air = 1.8 \times 10-5 Nsm-$2]

Options:

A) 250.6 ms$-$1

B) 43.56 ms$-$1

C) 4.94 ms$-$1

D) 14.4 ms$-$1

117

Medium

A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of cross-sectional area 'a' is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is (a < < A) :

Options:

A) {A \over {2a}}

B) None of these

C) {{2a} \over A}

D) {{a} \over A}

118

Easy

A body takes 4 min. to cool from 61$^\circ C to 59^\circ C. If the temperature of the surroundings is 30^\circ C, the time taken by the body to cool from 51^\circ C to 49^\circ$ C is :

Options:

A) 4 min.

B) 3 min.

C) 8 min.

D) 6 min.

119

Medium

Two spherical soap bubbles of radii r1 and r2 in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to :

Options:

A) {{{r_1}{r_2}} \over {{r_1} + {r_2}}}

B) \sqrt {{r_1}{r_2}}

C) \sqrt {r_1^2 + r_2^2}

D) {{{r_1} + {r_2}} \over 2}

120

Medium

Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are Y1 and Y2. The combination behaves as a single wire then its Young's modulus is :

Options:

A) Y = {{2{Y_1}{Y_2}} \over {3({Y_1} + {Y_2})}}

B) Y = {{2{Y_1}{Y_2}} \over {{Y_1} + {Y_2}}}

C) Y = {{{Y_1}{Y_2}} \over {2({Y_1} + {Y_2})}}

D) Y = {{{Y_1}{Y_2}} \over {{Y_1} + {Y_2}}}

121

Medium

The length of a metal wire is l1, when the tension in it is T1 and is l2 when the tension is T2. The natural length of the wire is :

Options:

A) \sqrt {{l_1}{l_2}}

B) {{{l_1}{T_2} - {l_2}{T_1}} \over {{T_2} - {T_1}}}

C) {{{l_1}{T_2} + {l_2}{T_1}} \over {{T_2} + {T_1}}}

D) {{{l_1} + {l_2}} \over 2}

122

Easy

Two small drops of mercury each of radius R coalesce to form a single large drop. The ratio of total surface energy before and after the change is :

Options:

A) {2^{{1 \over 3}}}:1

B) 1:{2^{{1 \over 3}}}

C) 2 : 1

D) 1 : 2

123

Medium

The value of tension in a long thin metal wire has been changed from T1 to T2. The lengths of the metal wire at two different values of tension T1 and T2 are l1 and l2 respectively. The actual length of the metal wire is :

Options:

A) {{{l_1} + {l_2}} \over 2}

B) \sqrt {{T_1}{T_2}{l_1}{l_2}}

C) {{{T_1}{l_2} - {T_2}{l_1}} \over {{T_1} - {T_2}}}

D) {{{T_1}{l_1} - {T_2}{l_2}} \over {{T_1} - {T_2}}}

124

Easy

An object is located at 2 km beneath the surface of the water. If the fractional compression ${{\Delta V} \over V} is 1.36%, the ratio of hydraulic stress to the corresponding hydraulic strain will be ____________. [Given : density of water is 1000 kgm-3 and g = 9.8 ms-$2]

Options:

A) 1.44 $\times 107 Nm-$2

B) 1.44 $\times 109 Nm-$2

C) 1.96 $\times 107 Nm-$2

D) 2.26 $\times 109 Nm-$2

125

Medium

When two soap bubbles of radii a and b (b > a) coalesce, the radius of curvature of common surface is :

Options:

A) {{b - a} \over {ab}}

B) {{a + b} \over {ab}}

C) {{ab} \over {a + b}}

D) {{ab} \over {b - a}}

126

Medium

What will be the nature of flow of water from a circular tap, when its flow rate increased from 0.18 L/min to 0.48 L/min? The radius of the tap and viscosity of water are 0.5 cm and 10$-$3 Pa s, respectively. (Density of water : 103 kg/m3)

Options:

A) Steady flow to unsteady flow

B) Unsteady to steady flow

C) Remains turbulent flow

D) Remains steady flow

127

Easy

The pressure acting on a submarine is 3 $\times 105 Pa at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be : (Assume that atmospheric pressure is 1 \times 105 Pa density of water is 103 kg m-3, g = 10 ms-$2)

Options:

A) {{200} \over 5}$%

B) {{200} \over 3}$%

C) {{3} \over 200}$%

D) {{5} \over 200}$%

128

Medium

The length of metallic wire is l1 when tension in it is T1. It is l2 when the tension is T2. The original length of the wire will be :

Options:

A) {{{T_1}{l_1} - {T_2}{l_2}} \over {{T_2} - {T_1}}}

B) {{{l_1} + {l_2}} \over 2}

C) {{{T_2}{l_1} + {T_1}{l_2}} \over {{T_1} + {T_2}}}

D) {{{T_2}{l_1} - {T_1}{l_2}} \over {{T_2} - {T_1}}}

129

Medium

A large number of water drops, each of radius r, combine to have a drop of radius R. If the surface tension is T and mechanical equivalent of heat is J, the rise in heat energy per unit volume will be :

Options:

A) {{2T} \over J}\left( {{1 \over r} - {1 \over R}} \right)

B) {{3T} \over J}\left( {{1 \over r} - {1 \over R}} \right)

C) {{3T} \over rJ}

D) {{2T} \over rJ}

130

Easy

The normal density of a material is $\rho$ and its bulk modulus of elasticity is K. The magnitude of increase in density of material, when a pressure P is applied uniformly on all sides, will be :

Options:

A) {{\rho K} \over P}

B) {{PK} \over \rho }

C) {{\rho P} \over K}

D) {K \over {\rho P}}

131

Medium

If Y, K and $\eta $ are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.

Options:

A) Y = {{9K\eta } \over {3K - \eta }}N/{m^2}

B) Y = {{9K\eta } \over {2\eta + 3K}}N/{m^2}

C) \eta = {{3YK} \over {9K + Y}}N/{m^2}

D) K = {{Y\eta } \over {9\eta - 3Y}}N/{m^2}

132

Medium

A fluid is flowing through a horizontal pipe of varying cross-section, with speed v ms–1 at a point where the pressure is P pascal. At another point where pressure is ${P \over 2} Pascal its speed is V ms–1. If the density of the fluid is \rho $ kg m–3 and the flow is streamline, then V is equal to :

Options:

A) \sqrt {{P \over {2\rho }} + {v^2}}

B) \sqrt {{P \over \rho } + {v^2}}

C) \sqrt {{{2P} \over \rho } + {v^2}}

D) \sqrt {{P \over \rho } + {v}}

133

Medium

An object of mass m is suspended at the end of a massless wire of length L and area of crosssection A. Young modulus of the material of the wire is Y. If the mass is pulled down slightly its frequency of oscillation along the vertical direction is :

Options:

A) f = {1 \over {2\pi }}\sqrt {{{YA} \over {mL}}}

B) f = {1 \over {2\pi }}\sqrt {{{mL} \over {YA}}}

C) f = {1 \over {2\pi }}\sqrt {{{YL} \over {mA}}}

D) f = {1 \over {2\pi }}\sqrt {{{mA} \over {YL}}}

134

Medium

In an experiment to verify Stokes law, a small spherical ball of radius r and density $\rho $ falls under gravity through a distance h in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of h is proportional to : (ignore viscosity of air)

Options:

A) r

B) r4

C) r3

D) r2

135

Medium

A hollow spherical shell at outer radius R floats just submerged under the water surface. The inner radius of the shell is r. If the specific gravity of the shell material is ${{27} \over 8}$ w.r.t water, the value of r is :

Options:

A) {{2} \over 3}$R

B) {{4} \over 9}$R

C) {{1} \over 3}$R

D) {{8} \over 9}$R

136

Medium

Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density d. The area of the base of both vessels is S but the height of liquid in one vessel is x1 and in the other, x2 . When both cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is:

Options:

A) gdS(x2 + x1)2

B) gdS$\left( {x_2^2 + x_1^2} \right)

C) {1 \over 4}gdS{\left( {{x_2} - {x_1}} \right)^2}

D) {3 \over 4}gdS{\left( {{x_2} - {x_1}} \right)^2}

137

Medium

A cube of metal is subjected to a hydrostatic pressure of 4 GPa. The percentage change in the length of the side of the cube is close to : (Given bulk modulus of metal, B = 8 $ \times $ 1010 Pa)

Options:

A) 0.6

B) 20

C) 1.67

D) 5

138

Medium

A air bubble of radius 1 cm in water has an upward acceleration 9.8 cm s–2. The density of water is 1 gm cm–3 and water offers negligible drag force on the bubble. The mass of the bubble is (g = 980 cm/s2).

Options:

A) 1.52 gm

B) 4.51 gm

C) 3.15 gm

D) 4.15 gm

139

Medium

A metallic sphere cools from 50oC to 40o in 300 s. If atmospheric temperature around is 20oC, then the sphere’s temperature after the next 5 minutes will be close to :

Options:

A) 35oC

B) 31oC

C) 33oC

D) 28oC

140

Medium

Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is :

Options:

A) 4 : 1

B) 8 : 1

C) 2 : 1

D) 0.8 : 1

141

Medium

A capillary tube made of glass of radius 0.15 mm is dipped vertically in a beaker filled with methylene iodide (surface tension = 0.05 Nm–1, density = 667 kg m–3) which rises to height h in the tube. It is observed that the two tangents drawn from liquid-glass interfaces (from opp. sides of the capillary) make an angle of 60o with one another. Then h is close to (g = 10 ms–2)

Options:

A) 0.049 m

B) 0.087 m

C) 0.137 m

D) 0.172 m

142

Medium

A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is 5 cm and the angular speed of rotation is $\omega $ rad s–1. The difference in the height, h (in cm) of liquid at the centre of vessel and at the side will be :

Options:

A) {{2{\omega ^2}} \over {25g}}

B) {{5{\omega ^2}} \over {2g}}

C) {{25{\omega ^2}} \over {2g}}

D) {{2{\omega ^2}} \over {5g}}

143

Medium

A small spherical droplet of density d is floating exactly half immersed in a liquid of density $\rho $ and surface tension T. The radius of the droplet is (take note that the surface tension applies an upward force on the droplet) :

Options:

A) r = \sqrt {{T \over {\left( {d - \rho } \right)g}}}

B) r = \sqrt {{{2T} \over {3\left( {d + \rho } \right)g}}}

C) r = \sqrt {{T \over {\left( {d + \rho } \right)g}}}

D) r = \sqrt {{{3T} \over {\left( {2d - \rho } \right)g}}}

144

Medium

Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1 : 4, the ratio of their diameters is:

Options:

A) 1 : 2

B) 2 : 1

C) 1:\sqrt 2

D) \sqrt 2 :1

145

Medium

Water flows in a horizontal tube (see figure). The pressure of water changes by 700 Nm–2 between A and B where the area of cross section are 40 cm2 and 20 cm2, respectively. Find the rate of flow of water through the tube. (density of water = 1000 kgm–3)

Options:

A) 1810 cm3/s

B) 2420 cm3/s

C) 3020 cm3/s

D) 2720 cm3/s

146

Medium

Two liquids of densities ${\rho _1} an {\rho _2} ({\rho _2} = 2{\rho _1}$) are filled up behind a square wall of side 10 m as shown in figure. Each liquid has a height of 5 m. The ratio of the forces due to these liquids exerted on upper part MN to that at the lower part NO is (Assume that the liquids are not mixing)

Options:

A) 1/3

B) 1/2

C) 1/4

D) 2/3

147

Medium

Consider a solid sphere of radius R and mass density $\rho \left( r \right) = {\rho _0}\left( {1 - {{{r^2}} \over {{R^2}}}} \right) , 0 < r \le R$ The minimum density of a liquid in which it will float is :

Options:

A) {{2{\rho _0}} \over 3}

B) {{2{\rho _0}} \over 5}

C) {{{\rho _0}} \over 5}

D) {{{\rho _0}} \over 3}

148

Medium

A leak proof cylinder of length 1m, made of a metal which has very low coefficient of expansion is floating vertically in water at 0°C such that its height above the water surface is 20 cm. When the temperature of water is increased to 4°C, the height of the cylinder above the water surface becomes 21 cm. The density of water at T = 4°C, relative to the density at T = 0°C is close to :

Options:

A) 1.04

B) 1.26

C) 1.01

D) 1.03

149

Medium

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4 cm and 4.8 cm, respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is :

Options:

A) {3 \over 4}

B) {9 \over {16}}

C) {{\sqrt 3 } \over 2}

D) {{81} \over {256}}

150

Medium

A solid sphere, of radius R acquires a terminal velocity v1 when falling (due to gravity) through a viscous fluid having a coefficient of viscosity . The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, v2, when falling through the same fluid, the ratio (v1/v2) equals :

Options:

A) {1 \over 9}

B) {1 \over {27}}

C) 27

D) 9

151

Medium

A uniform cylindrical rod of length L and radius r, is made from a material whose Young’s modulus of Elasticity equals Y. When this rod is heated by temperature T and simultaneously subjected to a net longitudinal compressional force F, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equal to :

Options:

A) {{3F} \over {\left( {\pi {r^2}YT} \right)}}

B) {{6F} \over {\left( {\pi {r^2}YT} \right)}}

C) {F \over {\left( {3\pi {r^2}YT} \right)}}

D) {9F\left( {\pi {r^2}YT} \right)}

152

Medium

The number density of molecules of a gas depends on their distance r from the origin as, $n\left( r \right) = {n_0}{e^{ - \alpha {r^4}}}$. Then the total number of molecules is proportional to :

Options:

A) {n_0}{\alpha ^{ - 3/4}}

B) {n_0}{\alpha ^{ - 3}}

C) {n_0}{\alpha ^{1/4}}

D) \sqrt {{n_0}} {\alpha ^{1/2}}

153

Medium

A submarine experiences a pressure of 5.05 × 106 Pa at a depth of d1 in a sea. When it goes further to a depth of d2, it experiences a pressure of 8.08 × 106 Pa. Then d2 –d1 is approximately (density of water = 103 kg/m3 and acceleration due to gravity = 10 ms–2 ) :

Options:

A) 600 m

B) 400 m

C) 300 m

D) 500 m

154

Medium

A cubical block of side 0.5 m floats on water with 30% of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water? [Take, density of water = 103 kg/m3]

Options:

A) 30.1 kg

B) 87.5 kg

C) 65.4 kg

D) 46.3 kg

155

Medium

The elastic limit of brass is 379 MPa. What should be the minimum diameter of a brass rod if it is to support a 400 N load without exceeding its elastic limit?

Options:

A) 1.16 mm

B) 1.36 mm

C) 1.00 mm

D) 0.90 mm

156

Medium

Water from a tap emerges vertically downwards with an initial speed of 1.0 ms–1 . The cross-sectional area of the tap is 10–4 m2. Assume that the pressure is constant throughout the stream of water and that the flow is streamlined. The cross-sectional area of the stream, 0.15 m below the tap would be : (Take g = 10 ms–2)

Options:

A) 5 × 10–4 m2

B) 2 × 10–5 m2

C) 5 × 10–5 m2

D) 1 × 10–5 m2

157

Medium

In an experiment, brass and steel wires of length 1 m each with areas of cross section 1mm2 are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress required to produce a net elongation of 0.2 mm is, [Given, the Young's Modulus for steel and brass are, respectively, 120 × 109 N/m2 and 60 × 109 N/m2]

Options:

A) 8.0 × 106 N/m2

B) 1.2 × 106 N/m2

C) 0.2 × 106 N/m2

D) 1.8 × 106 N/m2

158

Medium

The ratio of surface tensions of mercury and water is given to be 7.5 while the ratio of thier densities is 13.6. Their contact angles, with glass, are close to 135° and 0°, respectively. It is observed that mercury gets depressed by an amount h in a capillary tube of radius r1, while water rises by the same amount h in a capillary tube of radius r2. The ratio, (r1/r2), is then close to :

Options:

A) 2/5

B) 2/3

C) 3/5

D) 4/5

159

Medium

A wooden block floating in a bucket of water has 4/5 of its volume submerged. When certain amount of an oil is poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water is :-

Options:

A) 0.8

B) 0.7

C) 0.6

D) 0.5

160

Medium

A simple pendulum oscillating in air has period T. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is 1/16 th of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is :

Options:

A) 2T\sqrt {{1 \over {10}}}

B) 4T\sqrt {{1 \over {14}}}

C) 4T\sqrt {{1 \over {15}}}

D) 2T\sqrt {{1 \over {14}}}

161

Medium

If 'M' is the mass of water that rises in a capillary tube of radius 'r', then mass of water which will rise in a capillary tube of radius '2r' is :

Options:

A) M

B) 4M

C) M/2

D) 2M

162

Medium

Young's moduli of two wires A and B are in the ratio 7 : 4. Wire A is 2 m long and has radius R. Wire B is 1.5 m long and has radius 2 mm. If the two wires stretch by the same length for a given load, then the value of R is close to :-

Options:

A) 1.7 mm

B) 1.9 mm

C) 1.3 mm

D) 1.5 mm

163

Medium

Water from a pipe is coming at a rate of 100 litres per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flow is of the order of : (density of water = 1000 kg/m3, coefficient of viscosity of water = 1mPas)

Options:

A) 106

B) 104

C) 103

D) 102

164

Medium

A steel wire having a radius of 2.0 mm, carrying a load of 4 kg, is hanging from a ceiling. Given that g = 3.1 p ms–2, what will be the tensile stress that would be developed in the wire ?

Options:

A) 3.1 × 106 Nm–2

B) 6.2 × 106 Nm–2

C) 4.8 × 106 Nm–2

D) 5.2 × 106 Nm–2

165

Medium

A boy's catapult is made of rubber cord which is 42 cm long, with 6 mm diameter of cross-section and of negligible mass. The boy keeps a stone weighing 0.02kg on it and stretches the cord by 20 cm by applying a constant force. When released, the stone flies off with a velocity of 20 ms–1. Neglect the change in the area of cross-section of the cord while stretched. The Young's modulus of rubber is closest to:

Options:

A) 104 Nm–2

B) 106 Nm–2

C) 108 Nm–2

D) 103 Nm–2

166

Medium

A load of mass M kg is suspended from a steel wire of length 2m and radius 1.0 mm in Searle's apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8. The new value of increase in length of the steel wire is:

Options:

A) 5.0 mm

B) zero

C) 3.0 mm

D) 4.0 mm

167

Medium

A soap bubble, blown by a mechanical pump at the mouth of a tube, increases in volume, with time, at a constant rate. The graph that correctly depicts the time dependence of pressure inside the bubble is given by :

Options:

168

Medium

A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be :

Options:

A) 2.0

B) 1.2

C) 0.1

D) 0.4

169

Medium

A liquid of density $\rho is coming out of a hose pipe of radius a with horizontal speed \upsilon $ and hits a mesh. 50% of the liquid passes through the mesh unaffected. 25% looses all of its momentum and 25% comes back with the same speed. The resultant pressure on the mesh will be :

Options:

A) {3 \over 4}\rho {v^2}

B) {1 \over 4}\rho {v^2}

C) {1 \over 2}\rho {v^2}

D) \rho {v^2}

170

Medium

Water flows into a large tank with flat bottom at the rate of 10–4m3s–1. Water is also leaking out of a hole ofarea 1 cm2 at its bottom. If the height of the water in the tank remains steady, then this height is -

Options:

A) 2.9 cm

B) 5.1 cm

C) 4 cm

D) 1.7 cm

171

Medium

The top of a water tank is open to air and its water level is mainted. It is giving out 0.74 m3 water per minute through a circular opening of 2 cm radius in its wall. The depth of the center of the opening from the level of water in the tank is close to :

Options:

A) 6.0 m

B) 4.8 m

C) 9.6 m

D) 2.9 m

172

Medium

A small soap bubble of radius 4 cm is trapped inside another bubble of radius 6 cm without any contact. Let P2 be the pressure inside the inner bubble and P0, the pressure outside the outer bubble. Radius of another bubble with pressure difference P2 $-$ P0 between its inside and outside would be :

Options:

A) 12 cm

B) 2.4 cm

C) 6 cm

D) 4.8 cm

173

Medium

A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, $\left( {{dr \over r}} \right)$ is:

Options:

A) {{mg} \over {Ka}}

B) {{Ka} \over {mg}}

C) {{Ka} \over {3mg}}

D) {{mg} \over {3Ka}}

174

Medium

When an air bubble of radius r rises from the bottom to the surface of a lake its radius becomes ${{5r} \over 4}.$ Taking the atmospheric pressure to be equal to 10 m height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature) :

Options:

A) 11.2 m

B) 8.7 m

C) 9.5 m

D) 10.5 m

175

Medium

As shown in the figure, forces of 105 N each are applied in opposite directions, on the upper and lower faces of a cube of side 10 cm, shifting the upper face parallel to itself by 0.5 cm. If the side of another cube of the same material is 20 cm, then under similar conditions as above, the displacement will be :

Options:

A) 0.25 cm

B) 0.37 cm

C) 0.75 cm

D) 1.00 cm

176

Medium

A body takes 10 minutes to cool from 60oC to 50oC. The tempertature of surroundings is constant at 25oC. Then, the temperature of the body after next 10 minutes will be approximately :

Options:

A) 47oC

B) 41oC

C) 45oC

D) 43oC

177

Medium

A thin uniform tube is bent into a circle of radius $r in the vertical plane. Equal volumes of two immiscible liquids, whose densities are {\rho _1} and {\rho _2} \left( {{\rho _1} > {\rho _2}} \right), fill half the circle. The angle \theta $ between the radius vector passing through the common interface and the vertical is :

Options:

A) \theta = {\tan ^{ - 1}}\pi \left( {{{{\rho _1}} \over {{\rho _2}}}} \right)

B) \theta = {\tan ^{ - 1}}{\pi \over 2}\left( {{{{\rho _1}} \over {{\rho _2}}}} \right)

C) \theta = {\tan ^{ - 1}}\left( {{{{\rho _1} - {\rho _2}} \over {{\rho _1} + {\rho _2}}}} \right)

D) \theta = {\tan ^{ - 1}}{\pi \over 2}\left( {{{{\rho _1} + {\rho _2}} \over {{\rho _1} - {\rho _2}}}} \right)

178

Medium

Two tubes of radii r1 and r2, and lengths l1 and l2 , respectively, are connected in series and a liquid flows through each of them in stream line conditions. P1 and P2 are pressure differences across the two tubes. If P2 is 4P1 and l2 is ${{{1_1}} \over 4}$, then the radius r2 will be equal to :

Options:

A) r1

B) 2r1

C) 4r1

D) {{{r_1}} \over 2}

179

Medium

A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of :

Options:

A) {1 \over {81}}

B) 9

C) {1 \over {9}}

D) 81

180

Medium

A bottle has an opening of radius a and length b. A cork of length b and radius (a + $\Delta a) where (\Delta a < < a) is compressed to fit into the opening completely (See figure). If the bulk modulus of cork is B and frictional coefficient between the bottle and cork is \mu $ then the force needed to push the cork into the bottle is :

Options:

A) ($\pi \mu B b) \Delta $a

B) (2$\pi \mu B b) \Delta $a

C) ($\pi \mu $ B b) a

D) (4$\pi \mu B b) \Delta $a

181

Medium

A thin 1 m long rod has a radius of 5 mm. A force of 50 $\pi $kN is applied at one end to determine its Young’s modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is 0.01 mm, which of the following statements is false ?

Options:

A) {{\Delta \gamma } \over \gamma }$ gets minimum contribution from the uncertainty in the length.

B) The figure of merit is the largest for the length of the rod.

C) The maximum value of $\gamma that can be determined is 2 \times $ 1014 N/m2

D) {{\Delta \gamma } \over \gamma }$ gets its maximum contribution from the uncertainty in strain

182

Medium

Consider a water jar of radius R that has water filled up to height H and is kept on astand of height h (see figure). Through a hole of radius r (r << R) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is x. Then :

Options:

A) x = r\left( {{H \over {H + h}}} \right)

B) x = r{\left( {{H \over {H + h}}} \right)^{{1 \over 2}}}

C) x = r{\left( {{H \over {H + h}}} \right)^{{1 \over 4}}}

D) x = r{\left( {{H \over {H + h}}} \right)^{{2}}}

183

Medium

A uniformly tapering conical wire is made from a material of Young’s modulus Y and has a normal, unextended length L. The radii, at the upper and lower ends of this conical wire, have values R and 3 R, respectively. The upper end of the wire is fixed to a rigid support and a mass M is suspended from its lower end. The equilibrium extended length, of this wire, would equal :

Options:

A) L $\left( {1 + {2 \over 9}{{Mg} \over {\pi Y{R^2}}}} \right)

B) L $\left( {1 + {1 \over 3}{{Mg} \over {\pi Y{R^2}}}} \right)

C) L $\left( {1 + {1 \over 9}{{Mg} \over {\pi Y{R^2}}}} \right)

D) L $\left( {1 + {2 \over 3}{{Mg} \over {\pi Y{R^2}}}} \right)

184

Medium

Which of the following option correctly describes the variation of the speed v and acceleration ‘a’ of a point mass falling vertically in a viscous medium that applies a force F = − kv, where ‘k’ is a constant, on the body ? (Graphs are schematic and not drawn to scale)

Options:

185

Medium

An open glass tube is immersed in mercury in such a way that a length of $8 cm extends above the mercury level. The open end of the tube is then closed and scaled and the tube is raised vertically up by additional 46 cm. What will be length of the air column above mercury in the tube now? (Atmospheric pressure =76 cm of Hg$)

Options:

A) 16 cm

B) 22 cm

C) 38 cm

D) 6 cm

186

Medium

On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius $R and making a circular contact of radius r with the bottom R and making a circular contact of radius r with the bottom of the vessel. If r < < R and the surface tension of water is T, value of r just before bubbles detach is: (density of water is {\rho _w}$)

Options:

A) {R^2}\sqrt {{{{\rho _w}g} \over {3T}}}

B) {R^2}\sqrt {{{{\rho _w}g} \over {6T}}}

C) {R^2}\sqrt {{{{\rho _w}g} \over {T}}}

D) {R^2}\sqrt {{{{2\rho _w}g} \over {3T}}}

187

Medium

The pressure that has to be applied to the ends of a steel wire of length $10 cm to keep its length constant when its temperature is raised by {100^ \circ }C is: (For steel Young's modulus is 2 \times {10^{11}}\,\,N{m^{ - 2}} and coefficient of thermal expansion is 1.1 \times {10^{ - 5}}\,{K^{ - 1}}$ )

Options:

A) 2.2 \times {10^8}\,\,Pa

B) 2.2 \times {10^9}\,\,Pa

C) 2.2 \times {10^7}\,\,Pa

D) 2.2 \times {10^6}\,\,Pa

188

Medium

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities ${d_1} and {d_2} are filled in the tube. Each liquid subtends {90^ \circ } angle at center. Radius joining their interface makes an angle \alpha with vertical. Radio {{{d_1}} \over {{d_2}}}$ is :

Options:

A) {{1 + \sin \,\alpha } \over {1 - \sin \,\alpha }}

B) {{1 + \cos \,\alpha } \over {1 - \cos \,\alpha }}

C) {{1 + \tan \,\alpha } \over {1 - \tan \,\alpha }}

D) {{1 + \sin \,\alpha } \over {1 - \cos \,\alpha }}

189

Medium

A uniform cylinder of length $L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a mass-less spring such that it is half submerged in a liquid of density \sigma at equilibrium position. The extension {x_0}$ of the spring when it is in equilibrium is:

Options:

A) {{Mg} \over k}

B) {{Mg} \over k}\left( {1 - {{LA\sigma } \over M}} \right)

C) {{Mg} \over k}\left( {1 - {{LA\sigma } \over {2M}}} \right)

D) {{Mg} \over k}\left( {1 + {{LA\sigma } \over M}} \right)

190

Medium

If a piece of metal is heated to temperature $\theta and then allowed to cool in a room which is at temperature {\theta _0}, the graph between the temperature T of the metal and time t$ will be closest to

Options:

191

Medium

A thin liquid film formed between a U-shaped wire and a light slider supports a weight of $1.5 \times {10^{ - 2}}\,\,N (see figure). The length of the slider is 30 cm$ and its weight negligible. The surface tension of the liquid film is

Options:

A) 0.0125\,\,N{m^{ - 1}}

B) 0.1\,\,N{m^{ - 1}}

C) 0.05\,\,N{m^{ - 1}}

D) 0.025\,\,N{m^{ - 1}}

192

Medium

A liquid in a beaker has temperature $\theta \left( t \right) at time t and {\theta _0} is temperature of surroundings, then according to Newton's law of cooling the correct graph between {\log _e}\left( {\theta - {\theta _0}} \right) and t$ is :

Options:

193

Medium

Water is flowing continuously from a tap having an internal diameter $8 \times {10^{ - 3}}\,\,m. The water velocity as it leaves the tap is 0.4\,\,m{s^{ - 1}} . The diameter of the water stream at a distance 2 \times {10^{ - 1}}\,\,m$ below the tap is close to :

Options:

A) 7.5 \times {10^{ - 3}}m

B) 9.6 \times {10^{ - 3}}m

C) 3.6 \times {10^{ - 3}}m

D) 5.0 \times {10^{ - 3}}m

194

Medium

Work done in increasing the size of a soap bubble from a radius of $3 cm to 5 cm is nearly (Surface tension of soap solution = 0.03N{m^{ - 1}},

Options:

A) 0.2\pi mJ

B) 2\pi mJ

C) 0.4\pi mJ

D) 4\pi mJ

195

Medium

A ball is made of a material of density $\rho where {\rho _{oil}}\, < \rho < {\rho _{water}} with {\rho _{oil}} and {\rho _{water}}$ representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position?

Options:

196

Medium

Two wires are made of the same material and have the same volume. However wire $1 has cross-sectional area A and wire 2 has cross-sectional area 3A. If the length of wire 1 increases by \Delta x on applying force F, how much force is needed to stretch wire 2$ by the same amount?

Options:

A) 4F

B) 6F

C) 9F

D) F

197

Medium

A spherical solid ball of volume $V is made of a material of density {\rho _1}. It is falling through a liquid of density {\rho _2}\left( {{\rho _2} < {\rho _1}} \right). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e., {F_{viscous}} = - k{v^2}\left( {k > 0} \right).$ The terminal speed of the ball is

Options:

A) \sqrt {{{Vg\left( {{\rho _1} - {\rho _2}} \right)} \over k}}

B) {{{Vg{\rho _1}} \over k}}

C) \sqrt {{{Vg{\rho _1}} \over k}}

D) {{Vg\left( {{\rho _1} - {\rho _2}} \right)} \over k}

198

Medium

A jar is filled with two non-mixing liquids $1 and 2 having densities {\rho _1} and {\rho _2} respectively. A solid ball, made of a material of density {\rho _3}, is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for {\rho _1} , {\rho _1} and {\rho _3}$ ?

Options:

A) {\rho _3} < {\rho _1} < \rho {}_2

B) {\rho _1} > {\rho _3} > \rho {}_2

C) {\rho _1} < {\rho _2} < \rho {}_3

D) {\rho _1} < {\rho _3} < \rho {}_2

199

Medium

A capillary tube (A) is dipped in water. Another identical tube (B) is dipped in a soap-water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?

Options:

200

Medium

A wire elongates by $l mm when a LOAD W is hanged from it. If the wire goes over a pulley and two weights W each are hung at the two ends, the elongation of the wire will be (in mm$)

Options:

A) l

B) 2l

C) zero

D) l/2

201

Medium

If the terminal speed of a sphere of gold (density $ = 19.5\,\,kg/{m^3}) is 0.2 m/s in a viscous liquid (density = 1.5\,\,kg/{m^3}, find the terminal speed of a sphere of silver (density = 10.5\,\,kg/{m^3}$) of the same size in the same liquid

Options:

A) 0.4 m/s

B) 0.133 m/s

C) 0.1 m/s

D) 0.2 m/s

202

Medium

A $20 cm long capillary tube is dipped in water. The water rises up to 8 cm.$ If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be

Options:

A) 10 cm

B) 8 cm

C) 20 cm

D) 4 cm

203

Medium

If $S is stress and Y$ is young's modulus of material of a wire, the energy stored in the wire per unit volume is

Options:

A) {{{S^2}} \over {2Y}}

B) 2{S^2}Y

C) {S \over {2Y}}

D) {{2Y} \over {{S^2}}}

204

Medium

If two soap bubbles of different radii are connected by a tube

Options:

A) air flows from the smaller bubble to the bigger

B) air flows from bigger bubble to the smaller bubble till the sizes are interchanged

C) air flows from the bigger bubble to the smaller bubble till the sizes become equal

D) there is no flow of air.

205

Medium

A wire fixed at the upper end stretches by length $l by applying a force F.$ The work done in stretching is

Options:

A) 2Fl

B) Fl

C) {F \over {2l}}

D) {{Fl} \over 2}

206

Medium

Spherical balls of radius $R are falling in a viscous fluid of viscosity \eta with a velocity v.$ The retarding viscous force acting on the spherical ball is

Options:

A) inversely proportional to both radius $R and velocity v

B) directly proportional to both radius $R and velocity v

C) directly proportional to $R but inversely proportional to v

D) inversely proportional to $R, but directly proportional to velocity v

207

Medium

According to Newton's law of cooling, the rate of cooling of a body is proportional to ${\left( {\Delta \theta } \right)^n}, where {\Delta \theta } is the difference of the temperature of the body and the surrounding, and n$ is equal to :

Options:

A) two

B) three

C) four

D) one

208

Medium

A cylinder of height $20 m is completely filled with water. The velocity of efflux of water (in m{s^{ - 1}}$) through a small hole on the side wall of the cylinder near its bottom is

Options:

A) 10

B) 20

C) 25.5

D) 5

209

Medium

A soap bubble of surface tension 0.04 \mathrm{~N} / \mathrm{m} is blown to a diameter of 7 cm . If (15000-x) \mu \mathrm{J} of work is done in blowing it further to make its diameter 14 cm , then the value of x is \_\_\_\_ . $ (\pi=22 / 7)

Options:

210

Medium

Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of 10 \mathrm{~cm} / \mathrm{s} coalesce to form a bigger drop. The terminal velocity of bigger drop is \_\_\_\_ \mathrm{cm} / \mathrm{s}.

Options:

211

Medium

A ball of radius r and density \rho dropped through a viscous liquid of density \sigma and viscosity \eta attains its terminal velocity at time t, given by t=A \rho^a r^b \eta^c \sigma^d, where A is a constant and a, b, c and d are integers. The value of \frac{b+c}{a+d} is \_\_\_\_ .

Options:

212

Easy

The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is 20 \mathrm{~cm} / \mathrm{s}. The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be \_\_\_\_ \mathrm{cm} / \mathrm{s}.

Options:

213

Medium

A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to a change of volume of 0.8 cm3. If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was _______ litre.(Take 1 atm = 105 Pa)

Options:

214

Medium

A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of a uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping the distance between wedge point and 200 gm weight as 25 cm. Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water. (Take the density of unknown mass is more than that of the water, the mass did not absorb water and water density is 1 gm/cm3.) The unknown mass is _____ kg.

Options:

215

Medium

Two slabs with square cross section of different materials (1,2) with equal sides (l) and thickness d_1 and d_2 such that d_2=2 d_1 and l>d_2. Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is \theta_2=2 \theta_1. If the shear moduli of material 1 is 4 \times 10^9 \mathrm{~N} / \mathrm{m}^2, then shear moduli of material 2 is x \times 10^9 \mathrm{~N} / \mathrm{m}^2, where value of x is ________.

Options:

216

Medium

The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is n times the volume of the bubble B, then, the value of n is__________.

Options:

217

Easy

The length of a light string is 1.4 m when the tension on it is 5 N . If the tension increases to 7 N , the length of the string is 1.56 m . The original length of the string is__________m.

Options:

218

Medium

A steel wire of length 2 m and Young's modulus 2.0 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2} is stretched by a force. If Poisson ratio and transverse strain for the wire are 0.2 and 10^{-3} respectively, then the elastic potential energy density of the wire is __________ \times 10^5 (in SI units).

Options:

219

Easy

A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of 100 \mathrm{~cm}^2 with hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density 1.5 \times 10^3 \mathrm{~kg} / \mathrm{m}^3. What force one needs to apply on the hinged door so that it does not get opened ? $\text { (Acceleration due to gravity }=10 \mathrm{~m} / \mathrm{s}^2 \text { ) }

Options:

220

Easy

The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure of 7 \times 10^{6} ~\mathrm{Pa}, would be __________ \mathrm{mm}{ }^3. (Given bulk modulus of copper =1.4 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2} )

Options:

221

Easy

In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of \left[M^a L^b T^c\right]. If b=3, the value of c is _________.

Options:

222

Easy

The increase in pressure required to decrease the volume of a water sample by 0.2 \% is \mathrm{P} \times 10^5 \mathrm{Nm}^{-2}. Bulk modulus of water is 2.15 \times 10^9 \mathrm{Nm}^{-2}. The value of P is _________ .

Options:

223

Medium

An air bubble of radius 1.0 mm is observed at a depth 20 cm below the free surface of a liquid having surface tension 0.095 \mathrm{~J} / \mathrm{m}^2 and density 10^3 \mathrm{~kg} / \mathrm{m}^3. The difference between pressure inside the bubble and atmospheric pressure is __________ \mathrm{N} / \mathrm{m}^2. (Take \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 )

Options:

224

Easy

Two soap bubbles of radius 2 cm and 4 cm , respectively, are in contact with each other. The radius of curvature of the common surface, in cm , is _________.

Options:

225

Easy

Two persons pull a wire towards themselves. Each person exerts a force of $200 \mathrm{~N} on the wire. Young's modulus of the material of wire is 1 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}. Original length of the wire is 2 \mathrm{~m} and the area of cross section is 2 \mathrm{~cm}^2. The wire will extend in length by _________ \mu \mathrm{m}$.

Options:

226

Medium

Small water droplets of radius $0.01 \mathrm{~mm} are formed in the upper atmosphere and falling with a terminal velocity of 10 \mathrm{~cm} / \mathrm{s}. Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new terminal velocity will be ________ \mathrm{cm} / \mathrm{s}$.

Options:

227

Easy

A liquid column of height $0.04 \mathrm{~cm} balances excess pressure of a soap bubble of certain radius. If density of liquid is 8 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3} and surface tension of soap solution is 0.28 \mathrm{~Nm}^{-1}, then diameter of the soap bubble is __________ \mathrm{cm}. (if \mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}$ )

Options:

228

Medium

A wire of cross sectional area A, modulus of elasticity $2 \times 10^{11} \mathrm{~Nm}^{-2} and length 2 \mathrm{~m} is stretched between two vertical rigid supports. When a mass of 2 \mathrm{~kg} is suspended at the middle it sags lower from its original position making angle \theta=\frac{1}{100} radian on the points of support. The value of A is ________ \times 10^{-4} \mathrm{~m}^2 (consider x<<\mathrm{L} ). (given : \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$)

Options:

229

Easy

A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of big drop is $\frac{10}{x}. The value of x$ is ________.

Options:

230

Easy

A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of $10 \mathrm{~N}$ is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is _________ N.

Options:

231

Medium

The density and breaking stress of a wire are $6 \times 10^4 \mathrm{~kg} / \mathrm{m}^3 and 1.2 \times 10^8 \mathrm{~N} / \mathrm{m}^2 respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is \frac{1}{3}^{\text {rd }} of the value on the surface of earth. The maximum length of the wire with breaking is _______ \mathrm{m} (take, \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$).

Options:

232

Easy

Mercury is filled in a tube of radius $2 \mathrm{~cm} up to a height of 30 \mathrm{~cm}. The force exerted by mercury on the bottom of the tube is _________ N. (Given, atmospheric pressure =10^5 \mathrm{~Nm}^{-2}, density of mercury =1.36 \times 10^4 \mathrm{~kg} \mathrm{~m}^{-3}, \mathrm{~g}=10 \mathrm{~m} \mathrm{~s}^{-2}, \pi=\frac{22}{7})

Options:

233

Medium

A soap bubble is blown to a diameter of $7 \mathrm{~cm}. 36960 \mathrm{~erg} of work is done in blowing it further. If surface tension of soap solution is 40 dyne/\mathrm{cm} then the new radius is ________ cm Take (\pi=\frac{22}{7})$.

Options:

234

Medium

An elastic spring under tension of $3 \mathrm{~N} has a length a. Its length is b under tension 2 \mathrm{~N}. For its length (3 a-2 b)$, the value of tension will be _______ N.

Options:

235

Easy

One end of a metal wire is fixed to a ceiling and a load of 2 \mathrm{~kg} hangs from the other end. A similar wire is attached to the bottom of the load and another load of 1 \mathrm{~kg} hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be ________. [Area of cross section of wire =0.005 \mathrm{~cm}^2, \mathrm{Y}=2 \times 10^{11} \mathrm{Nm}^{-2} and \mathrm{g}=10 \mathrm{~ms}^{-2} ]

Options:

236

Medium

A plane is in level flight at constant speed and each of its two wings has an area of 40 \mathrm{~m}^2. If the speed of the air is 180 \mathrm{~km} / \mathrm{h} over the lower wing surface and 252 \mathrm{~km} / \mathrm{h} over the upper wing surface, the mass of the plane is ___________ kg. (Take air density to be 1 \mathrm{~kg} \mathrm{~m}^{-3} and \mathrm{g}=10 \mathrm{~ms}^{-2} )

Options:

237

Medium

Two blocks of mass $2 \mathrm{~kg} and 4 \mathrm{~kg} are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is 4.0 \times 10^{-5} \mathrm{~m} and Young's modulus of the metal is 2.0 \times 10^{11} \mathrm{~N} / \mathrm{m}^2. The longitudinal strain developed in the wire is \frac{1}{\alpha \pi}. The value of \alpha is _________. [Use g=10 \mathrm{~m} / \mathrm{s}^2$]

Options:

238

Easy

The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by $0.02 \% is _______ m. (Take density of sea water =10^3 \mathrm{kgm}^{-3}, Bulk modulus of rubber =9 \times 10^8 \mathrm{~Nm}^{-2}, and g=10 \mathrm{~ms}^{-2}$)

Options:

239

Easy

A big drop is formed by coalescing 1000 small identical drops of water. If $E_1 be the total surface energy of 1000 small drops of water and E_2 be the surface energy of single big drop of water, then E_1: E_2 is x: 1 where x=$ ________.

Options:

240

Medium

Each of three blocks $\mathrm{P}, \mathrm{Q} and \mathrm{R} shown in figure has a mass of 3 \mathrm{~kg}. Each of the wires \mathrm{A} and \mathrm{B} has cross-sectional area 0.005 \mathrm{~cm}^2 and Young's modulus 2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}. Neglecting friction, the longitudinal strain on wire B is ________ \times 10^{-4}. (Take \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$)

Options:

241

Medium

Two metallic wires $P and Q have same volume and are made up of same material. If their area of cross sections are in the ratio 4: 1 and force F_1 is applied to P, an extension of \Delta l is produced. The force which is required to produce same extension in Q is \mathrm{F}_2. The value of \frac{F_1}{F_2}$ is _________.

Options:

242

Easy

In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are $70 \mathrm{~ms}^{-1} and 65 \mathrm{~ms}^{-1} respectively. If the wing area is 2 \mathrm{~m}^2, the lift of the wing is _________ N. (Given density of air =1.2 \mathrm{~kg} \mathrm{~m}^{-3}$)

Options:

243

Easy

The reading of pressure metre attached with a closed pipe is $4.5 \times 10^4 \mathrm{~N} / \mathrm{m}^2. On opening the valve, water starts flowing and the reading of pressure metre falls to 2.0 \times 10^4 \mathrm{~N} / \mathrm{m}^2. The velocity of water is found to be \sqrt{V} \mathrm{~m} / \mathrm{s}. The value of V$ is _________.

Options:

244

Easy

If average depth of an ocean is $4000 \mathrm{~m} and the bulk modulus of water is 2 \times 10^9 \mathrm{~Nm}^{-2}, then fractional compression \frac{\Delta V}{V} of water at the bottom of ocean is \alpha \times 10^{-2}. The value of \alpha is _______ (Given, \mathrm{g}=10 \mathrm{~ms}^{-2}, \rho=1000 \mathrm{~kg} \mathrm{~m}^{-3}$)

Options:

245

Easy

There is an air bubble of radius 1.0 \mathrm{~mm} in a liquid of surface tension 0.075~ \mathrm{Nm}^{-1} and density 1000 \mathrm{~kg} \mathrm{~m}^{-3} at a depth of 10 \mathrm{~cm} below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is _________ \mathrm{Pa}\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)

Options:

246

Medium

The elastic potential energy stored in a steel wire of length $20 \mathrm{~m} stretched through 2 \mathrm{~cm} is 80 \mathrm{~J}. The cross sectional area of the wire is __________ \mathrm{mm}^{2}. \left(\right. Given, \left.y=2.0 \times 10^{11} \mathrm{Nm}^{-2}\right)

Options:

247

Medium

Glycerin of density $1.25 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3} is flowing through the conical section of pipe The area of cross-section of the pipe at its ends are 10 \mathrm{~cm}^{2} and 5 \mathrm{~cm}^{2} and pressure drop across its length is 3 ~\mathrm{Nm}^{-2}. The rate of flow of glycerin through the pipe is x \times 10^{-5} \mathrm{~m}^{3} \mathrm{~s}^{-1}. The value of x$ is ___________.

Options:

248

Medium

The surface tension of soap solution is $3.5 \times 10^{-2} \mathrm{~Nm}^{-1}. The amount of work done required to increase the radius of soap bubble from 10 \mathrm{~cm} to 20 \mathrm{~cm} is _________ \times ~10^{-4} \mathrm{~J}. (\operatorname{take} \pi=22 / 7)

Options:

249

Medium

A wire of density $8 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3} is stretched between two clamps 0.5 \mathrm{~m} apart. The extension developed in the wire is 3.2 \times 10^{-4} \mathrm{~m}. If Y=8 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}, the fundamental frequency of vibration in the wire will be ___________ \mathrm{Hz}$.

Options:

250

Medium

The length of a wire becomes $l_{1} and l_{2} when 100 \mathrm{~N} and 120 \mathrm{~N} tensions are applied respectively. If 10 ~l_{2}=11~ l_{1}, the natural length of wire will be \frac{1}{x} ~l_{1}. Here the value of x$ is _____________.

Options:

251

Easy

Figure below shows a liquid being pushed out of the tube by a piston having area of cross section $2.0 \mathrm{~cm}^{2}. The area of cross section at the outlet is 10 \mathrm{~mm}^{2}. If the piston is pushed at a speed of 4 \mathrm{~cm} \mathrm{~s}^{-1}, the speed of outgoing fluid is __________ \mathrm{cm} \mathrm{s}^{-1}

Options:

252

Medium

Two wires each of radius 0.2 cm and negligible mass, one made of steel and the other made of brass are loaded as shown in the figure. The elongation of the steel wire is __________ $\times 10^{-6} m. [Young's modulus for steel = 2 \times 10^{11} Nm^{-2} and g = 10 ms^{-2}$ ]

Options:

253

Easy

An air bubble of diameter $6 \mathrm{~mm} rises steadily through a solution of density 1750 \mathrm{~kg} / \mathrm{m}^{3} at the rate of 0.35 \mathrm{~cm} / \mathrm{s}. The co-efficient of viscosity of the solution (neglect density of air) is ___________ Pas (given, \mathrm{g}=10 \mathrm{~ms}^{-2}$ ).

Options:

254

Easy

A metal block of mass $\mathrm{m} is suspended from a rigid support through a metal wire of diameter 14 \mathrm{~mm}. The tensile stress developed in the wire under equilibrium state is 7 \times 10^{5} \mathrm{Nm}^{-2}. The value of mass \mathrm{m} is _________ \mathrm{kg}. (Take, \mathrm{g}=9.8 \mathrm{~ms}^{-2} and \pi=\frac{22}{7}$ )

Options:

255

Easy

A steel rod has a radius of $20 \mathrm{~mm} and a length of 2.0 \mathrm{~m}. A force of 62.8 ~\mathrm{kN} stretches it along its length. Young's modulus of steel is 2.0 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}. The longitudinal strain produced in the wire is _____________ \times 10^{-5}

Options:

256

Easy

The surface of water in a water tank of cross section area $750 \mathrm{~cm}^{2} on the top of a house is h \mathrm{~m} above the tap level. The speed of water coming out through the tap of cross section area 500 \mathrm{~mm}^{2} is 30 \mathrm{~cm} / \mathrm{s}. At that instant, \frac{d h}{d t} is x \times 10^{-3} \mathrm{~m} / \mathrm{s}. The value of x$ will be ____________.

Options:

257

Easy

A certain pressure '$\mathrm{P}' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to 0.01 \% whereas the liquid gets compressed to 0.03 \%. The ratio of Bulk modulus of water to that of the liquid is \frac{3}{x}. The value of x$ is ____________.

Options:

258

Medium

A thin rod having a length of $1 \mathrm{~m} and area of cross-section 3 \times 10^{-6} \mathrm{~m}^{2} is suspended vertically from one end. The rod is cooled from 210^{\circ} \mathrm{C} to 160^{\circ} \mathrm{C}. After cooling, a mass \mathrm{M} is attached at the lower end of the rod such that the length of rod again becomes 1 \mathrm{~m}. Young's modulus and coefficient of linear expansion of the rod are 2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2} and 2 \times 10^{-5} \mathrm{~K}^{-1}, respectively. The value of \mathrm{M} is __________ \mathrm{kg}. (Take \mathrm{g=10~m~s^{-2}}$)

Options:

259

Easy

A metal block of base area 0.20 m$^2 is placed on a table, as shown in figure. A liquid film of thickness 0.25 mm is inserted between the block and the table. The block is pushed by a horizontal force of 0.1 N and moves with a constant speed. IF the viscosity of the liquid is 5.0\times10^{-3}~\mathrm{Pl}, the speed of block is ____________ \times10^{-3}$ m/s.

Options:

260

Medium

A body cools from 60$^\circC to 40^\circC in 6 minutes. If, temperature of surroundings is 10^\circC. Then, after the next 6 minutes, its temperature will be ____________^\circ$C.

Options:

261

Easy

A spherical drop of liquid splits into 1000 identical spherical drops. If u$_\mathrm{i} is the surface energy of the original drop and u_\mathrm{f} is the total surface energy of the resulting drops, the (ignoring evaporation), {{{u_f}} \over {{u_i}}} = \left( {{{10} \over x}} \right)$. Then value of x is ____________ :

Options:

262

Medium

As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of 45$^\circ with the load axis. The length of wire is 62.8 cm and its diameter is 4 mm. The Young's modulus is found to be x\times10^4 Nm^{-2}. The value of x$ is ___________.

Options:

263

Medium

A Spherical ball of radius 1mm and density 10.5 g/cc is dropped in glycerine of coefficient of viscosity 9.8 poise and density 1.5 g/cc. Viscous force on the ball when it attains constant velocity is $3696\times10^{-x} N. The value of x is ________. (Given, g = 9.8 m/s^2 and \pi=\frac{22}{7}$)

Options:

264

Medium

A tube of length $50 \mathrm{~cm} is filled completely with an incompressible liquid of mass 250 \mathrm{~g} and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity x \sqrt{F} \,\mathrm{rad} \,\mathrm{s}^{-1}. If \mathrm{F} be the force exerted by the liquid at the other end then the value of x$ will be __________.

Options:

265

Easy

A metal wire of length $0.5 \mathrm{~m} and cross-sectional area 10^{-4} \mathrm{~m}^{2} has breaking stress 5 \times 10^{8} \,\mathrm{Nm}^{-2}. A block of 10 \mathrm{~kg} is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be _________ \mathrm{ms}^{-1}$.

Options:

266

Easy

The velocity of a small ball of mass $0.3 \mathrm{~g} and density 8 \mathrm{~g} / \mathrm{cc} when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 1.3 \mathrm{~g} / \mathrm{cc}, then the value of viscous force acting on the ball will be x \times 10^{-4} \mathrm{~N}, The value of x is _________. [use \left.\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right]

Options:

267

Medium

The speed of a transverse wave passing through a string of length $50 \mathrm{~cm} and mass 10 \mathrm{~g} is 60 \mathrm{~ms}^{-1}. The area of cross-section of the wire is 2.0 \mathrm{~mm}^{2} and its Young's modulus is 1.2 \times 10^{11} \mathrm{Nm}^{-2}. The extension of the wire over its natural length due to its tension will be x \times 10^{-5} \mathrm{~m}. The value of x$ is __________.

Options:

268

Medium

A string of area of cross-section $4 \mathrm{~mm}^{2} and length 0.5 \mathrm{~m} is connected with a rigid body of mass 2 \mathrm{~kg}. The body is rotated in a vertical circular path of radius 0.5 \mathrm{~m}. The body acquires a speed of 5 \mathrm{~m} / \mathrm{s} at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is _________ \times 10^{-5}. (use Young's modulus 10^{11} \mathrm{~N} / \mathrm{m}^{2} and \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$)

Options:

269

Medium

The diameter of an air bubble which was initially $2 \mathrm{~mm}, rises steadily through a solution of density 1750 \mathrm{~kg} \mathrm{~m}^{-3} at the rate of 0.35 \,\mathrm{cms}^{-1}$. The coefficient of viscosity of the solution is _________ poise (in nearest integer). (the density of air is negligible).

Options:

270

Medium

In an experiment to determine the Young's modulus, steel wires of five different lengths $(1,2,3,4, and 5 \mathrm{~m}) but of same cross section \left(2 \mathrm{~mm}^{2}\right) were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is x \times 10^{11} \,\mathrm{Nm}^{-2}, then the value of x$ is __________.

Options:

271

Easy

A spherical soap bubble of radius 3 cm is formed inside another spherical soap bubble of radius 6 cm. If the internal pressure of the smaller bubble of radius 3 cm in the above system is equal to the internal pressure of the another single soap bubble of radius r cm. The value of r is ___________.

Options:

272

Medium

A square aluminum (shear modulus is $25 \times 10^{9}\, \mathrm{Nm}^{-2}) slab of side 60 \mathrm{~cm} and thickness 15 \mathrm{~cm} is subjected to a shearing force (on its narrow face) of 18.0 \times 10^{4} \mathrm{N}. The lower edge is riveted to the floor. The displacement of the upper edge is ____________ \mu$m.

Options:

273

Easy

A uniform heavy rod of mass $20 \mathrm{~kg}, cross sectional area 0.4 \mathrm{~m}^{2} and length 20 \mathrm{~m} is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is x \times 10^{-9} \mathrm{~m}. The value of x is _______________. (Given, young modulus Y = 2 \times 1011 Nm-2 and g = 10 ms-$2)

Options:

274

Medium

In an experiment to determine the Young's modulus of wire of a length exactly $1 \mathrm{~m}, the extension in the length of the wire is measured as 0.4 \mathrm{~mm} with an uncertainty of \pm\, 0.02 \mathrm{~mm} when a load of 1 \mathrm{~kg} is applied. The diameter of the wire is measured as 0.4 \mathrm{~mm} with an uncertainty of \pm \,0.01 \mathrm{~mm}. The error in the measurement of Young's modulus (\Delta \mathrm{Y}) is found to be x \times 10^{10}\, \mathrm{Nm}^{-2}. The value of x is _________________. \left(\right.take \mathrm{g}=10 \mathrm{~ms}^{-2}$ )

Options:

275

Easy

A wire of length $\mathrm{L} and radius \mathrm{r} is clamped rigidly at one end. When the other end of the wire is pulled by a force \mathrm{F}, its length increases by 5 \mathrm{~cm}. Another wire of the same material of length 4 \mathrm{L} and radius 4 \mathrm{r} is pulled by a force 4 \mathrm{F} under same conditions. The increase in length of this wire is __________________ \mathrm{cm}$.

Options:

276

Easy

The excess pressure inside a liquid drop is 500 Nm$-2. If the radius of the drop is 2 mm, the surface tension of liquid is x \times 10-3 Nm-$1. The value of x is _____________.

Options:

277

Medium

A small spherical ball of radius 0.1 mm and density 104 kg m$-3 falls freely under gravity through a distance h before entering a tank of water. If, after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of h will be ___________ m. (Given g = 10 ms-2, viscosity of water = 1.0 \times 10-5 N-sm-$2).

Options:

278

Easy

A liquid of density 750 kgm$-3 flows smoothly through a horizontal pipe that tapers in cross-sectional area from A1 = 1.2 \times 10-2 m2 to A2 = {{{A_1}} \over 2}. The pressure difference between the wide and narrow sections of the pipe is 4500 Pa. The rate of flow of liquid is ___________ \times 10-3 m3s-$1.

Options:

279

Easy

The area of cross-section of a large tank is 0.5 m2. It has a narrow opening near the bottom having area of cross-section 1 cm2. A load of 25 kg is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of water level in the tank is 40 cm above the bottom, will be ___________ cms$-1. [Take g = 10 ms-$2]

Options:

280

Medium

The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of 5 $\times 10-4 is __________ kJ/m3. Assume that material is elastic upto the linear strain of 5 \times 10-$4.

Options:

281

Easy

The elongation of a wire on the surface of the earth is 10$-4 m. The same wire of same dimensions is elongated by 6 \times 10-5 m on another planet. The acceleration due to gravity on the planet will be ____________ ms-2. (Take acceleration due to gravity on the surface of earth = 10 ms-$2)

Options:

282

Medium

An ideal fluid of density 800 kgm$-3, flows smoothly through a bent pipe (as shown in figure) that tapers in cross-sectional area from a to {a \over 2}. The pressure difference between the wide and narrow sections of pipe is 4100 Pa. At wider section, the velocity of fluid is {{\sqrt x } \over 6} ms-1 for x = ___________. (Given g = 10 ms-$2)

Options:

283

Easy

The velocity of upper layer of water in a river is 36 kmh$-1. Shearing stress between horizontal layers of water is 10-3 Nm-2. Depth of the river is __________ m. (Co-efficient of viscosity of water is 10-$2 Pa.s)

Options:

284

Medium

In an experiment to verify Newton's law of cooling, a graph is plotted between the temperature difference ($\DeltaT) of the water and surroundings and time as shown in figure. The initial temperature of water is taken as 80^\circ$C. The value of t2 as mentioned in the graph will be __________.

Options:

285

Easy

A steel rod with y = 2.0 $\times 1011 Nm-2 and \alpha = 10-5 ^\circC-1 of length 4 m and area of cross-section 10 cm2 is heated from 0^\circC to 400^\circC without being allowed to extend. The tension produced in the rod is x \times$ 105 N where the value of x is ____________.

Options:

286

Easy

When a rubber ball is taken to a depth of __________m in deep sea, its volume decreases by 0.5%. (The bulk modulus of rubber = 9.8 $\times 108 Nm-2, Density of sea water = 103 kgm-$3, g = 9.8 m/s2)

Options:

287

Medium

Wires W1 and W2 are made of same material having the breaking stress of 1.25 $\times 109 N/m2. W1 and W2 have cross-sectional area of 8 \times 10-7 m2 and 4 \times 10-$7 m2, respectively. Masses of 20 kg and 10 kg hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is ____________ kg. (Use g = 10 m/s2)

Options:

288

Medium

A soap bubble of radius 3 cm is formed inside the another soap bubble of radius 6 cm. The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is ................ cm.

Options:

289

Medium

The water is filled upto height of 12 m in a tank having vertical sidewalls. A hole is made in one of the walls at a depth 'h' below the water level. The value of 'h' for which the emerging steam of water strikes the ground at the maximum range is ________ m.

Options:

290

Medium

A stone of mass 20 g is projected from a rubber catapult of length 0.1 m and area of cross section 10$-6 m2 stretched by an amount 0.04 m. The velocity of the projected stone is ______________ m/s.(Young's modulus of rubber = 0.5 \times$ 109 N/m2)

Options:

291

Medium

In 5 minutes, a body cools from 75$^\circC to 65^\circC at room temperature of 25^\circC. The temperature of body at the end of next 5 minutes is _________^\circ$ C.

Options:

292

Medium

Consider a water tank as shown in the figure. It's cross-sectional area is 0.4 m2. The tank has an opening B near the bottom whose cross-section area is 1 cm2. A load of 24 kg is applied on the water at the top when the height of the water level is 40 cm above the bottom, the velocity of water coming out the opening B is v ms-1.The value of v, to the nearest integer, is ___________. [Take value of g to be 10 ms-2]

Options:

293

Medium

Two separate wires A and B are stretched by 2 mm and 4 mm respectively, when they are subjected to a force of 2 N. Assume that both the wires are made up of same material and the radius of wire B is 4 times that of the radius of wire A. The length of the wires A and B are in the ratio of a : b. Then a/b can be expressed as 1/x where x is _________.

Options:

294

Medium

Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes 0.01 cm3 of oleic acid per cm3 of the solution. Then you make a thin film of this solution (monomolecular thickness) of area 4 cm2 by considering 100 spherical drops of radius ${\left( {{3 \over {40\pi }}} \right)^{{1 \over 3}}} \times {10^{ - 3}} cm. Then the thickness of oleic acid layer will be x \times 10-$14 m. Where x is ____________.

Options:

295

Easy

A uniform metallic wire is elongated by 0.04 m when subjected to a linear force F. The elongation, if its length and diameter is doubled and subjected to the same force will be ________ cm.

Options:

296

Medium

A hydraulic press can lift 100 kg when a mass 'm' is placed on the smaller piston. It can lift ___________ kg when the diameter of the larger piston is increased by 4 times and that of the smaller piston is decreased by 4 times keeping the same mass 'm' on the smaller piston.

Options:

297

Medium

When a long glass capillary tube of radius 0.015 cm is dipped in a liquid, the liquid rises to a height of 15 cm within it. If the contact angle between the liquid and glass to close to 0o, the surface tension of the liquid, in milliNewton m–1, is [$\rho $(liquid) = 900 kgm–3, g = 10 ms–2] (Give answer in closest integer) _____.

Options:

298

Medium

A wire of density 9 $ \times 10–3 kg cm–3 is stretched between two clamps 1 m apart. The resulting strain in the wire is 4.9 \times 10–4. The lowest frequency of the transverse vibrations in the wire is : (Young’s modulus of wire Y = 9 \times $ 1010 Nm–2), (to the nearest integer), _________

Options:

299

Hard

Consider a water tank shown in the figure. It has one wall at x=L and can be taken to be very wide in the z direction. When filled with a liquid of surface tension S and density \rho, the liquid surface makes angle \theta_0\left(\theta_0 \ll 1\right) with the x-axis at x=L. If y(x) is the height of the surface then the equation for y(x) is: (take \theta(x)=\sin \theta(x)=\tan \theta(x)=\frac{d y}{d x}, g is the acceleration due to gravity)

Options:

A) \frac{d^2 y}{d x^2}=\sqrt{\frac{\rho g}{s}}

B) \frac{d y}{d x}=\sqrt{\frac{\rho g}{s}} x

C) \frac{d^2 y}{d x^2}=\frac{\rho g}{s} x

D) \frac{d^2 y}{d x^2}=\frac{\rho g}{s} y

300

Medium

An ideal fluid is flowing in a non-uniform cross-sectional tube $X Y (as shown in the figure) from end X to end Y. If K_1 and K_2 are the kinetic energy per unit volume of the fluid at X and Y$ respectively, then the correct option is :

Options:

A) K_1=K_2

B) 2 K_1=K_2

C) K_1>K_2

D) K_1 < K_2

301

Medium

The maximum elongation of a steel wire of $1 \mathrm{~m} length if the elastic limit of steel and its Young's modulus, respectively, are 8 \times 10^8 \mathrm{~N} \mathrm{~m}^{-2} and 2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$, is:

Options:

A) 4 mm

B) 0.4 mm

C) 40 mm

D) 8 mm

302

Medium

A thin flat circular disc of radius $4.5 \mathrm{~cm} is placed gently over the surface of water. If surface tension of water is 0.07 \mathrm{~N} \mathrm{~m}^{-1}$, then the excess force required to take it away from the surface is

Options:

A) 19.8 mN

B) 198 N

C) 1.98 mN

D) 99 N

303

Medium

A metallic bar of Young's modulus, $0.5 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2} and coefficient of linear thermal expansion 10^{-5}{ }^{\circ} \mathrm{C}^{-1}, length 1 \mathrm{~m} and area of cross-section 10^{-3} \mathrm{~m}^2 is heated from 0^{\circ} \mathrm{C} to 100^{\circ} \mathrm{C}$ without expansion or bending. The compressive force developed in it is :

Options:

A) 5 \times 10^3 \mathrm{~N}

B) 50 \times 10^3 \mathrm{~N}

C) 100 \times 10^3 \mathrm{~N}

D) 2 \times 10^3 \mathrm{~N}

304

Medium

The amount of elastic potential energy per unit volume (in SI unit) of a steel wire of length $100 \mathrm{~cm} to stretch it by 1 \mathrm{~mm} is (if Young's modulus of the wire =2.0 \times 10^{11} \mathrm{Nm}^{-2}$ ) :

Options:

A) 10^{11}

B) 10^{17}

C) 10^7

D) 10^5

305

Medium

Which of the following statement is not true?

Options:

A) Coefficient of viscosity is a scalar quantity

B) Surface tension is a scalar quantity

C) Pressure is a vector quantity

D) Relative density is a scalar quantity

306

Medium

The viscous drag acting on a metal sphere of diameter $1 \mathrm{~mm}, falling through a fluid of viscosity 0.8 \mathrm{~Pa} s with a velocity of 2 \mathrm{~m} \mathrm{~s}^{-1}$ is equal to :

Options:

A) 15 \times 10^{-3} \mathrm{~N}

B) 30 \times 10^{-3} \mathrm{~N}

C) 1.5 \times 10^{-3} \mathrm{~N}

D) 20 \times 10^{-3} \mathrm{~N}

307

Medium

The amount of energy required to form a soap bubble of radius $2 \mathrm{~cm} from a soap solution is nearly: (surface tension of soap solution =0.03 \mathrm{~N} \mathrm{~m}^{-1}$ )

Options:

A) 5.06 \times 10^{-4} \mathrm{~J}

B) 3.01 \times 10^{-4} \mathrm{~J}

C) 50.1 \times 10^{-4} \mathrm{~J}

D) 30.16 \times 10^{-4} \mathrm{~J}

308

Medium

The venturi-meter works on :

Options:

A) Bernoulli's principle

B) The principle of parallel axes

C) The principle of perpendicular axes

D) Huygen's principle

309

Medium

Let a wire be suspended from the ceiling (rigid support) and stretched by a weight $W attached at its free end. The longitudinal stress at any point of cross-sectional area A$ of the wire is :

Options:

A) W / A

B) W / 2 A

C) Zero

D) 2 W / A

310

Medium

Two copper vessels A and B have the same base area but of different shapes. A takes twice the volume of water as that B requires to fill upto a particular common height. Then the correct statement among the following is :

Options:

A) Vessel B weighs twice that of A.

B) Pressure on the base area of vessels A and B is same.

C) Pressure on the base area of vessels A and B is not same.

D) Both vessels A and B weigh the same.

311

Medium

The terminal velocity of a copper ball of radius 5 mm falling through a tank of oil at room temperature is 10 cm s$-1. If the viscosity of oil at room temperature is 0.9 kg m-1 s-$1, the viscous drag force is :

Options:

A) 4.23 $\times 10-$6 N

B) 8.48 $\times 10-$3 N

C) 8.48 $\times 10-$5 N

D) 4.23 $\times 10-$3 N

312

Medium

A spherical ball is dropped in a long column of a highly viscous liquid. The curve in the graph shown, which represents the speed of the ball (v) as a function of time (t) is

Options:

A) A

B) B

C) C

D) D

313

Medium

If a soap bubble expands, the pressure inside the bubble

Options:

A) Decreases

B) Increases

C) Remains the same

D) Is equal to the atmospheric pressure

314

Medium

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The stretching of a spring is determined by the shear modulus of the material of the spring. Reason (R) : A coil spring of copper has more tensile strength than a steel spring of same dimensions. In the light of the above statements, choose the most appropriate answer from the options given below:

Options:

A) Both (A) and (R) are true and (R) is the correct explanation of (A)

B) Both (A) and (R) are true and (R) is not the correct explanation of (A)

C) (A) is true but (R) is false

D) (A) is false but (R) is true

315

Medium

The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerin becomes constant after some time. If the density of glycerin is ${d \over 2}$, then the viscous force acting on the ball will be :

Options:

A) 2Mg

B) {{Mg} \over 2}

C) Mg

D) {{3} \over 2}$Mg

316

Medium

A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5 g. Another capillary tube of radius 2r is immersed in Water. The mass of water that will rise in this tube is :

Options:

A) 5.0 g

B) 10.0 g

C) 20.0 g

D) 2.5 g

317

Medium

A wire of length L, are of cross section A is hanging from a fixed support. The length of the wire changed to L1 when mass M is suspended from its free end. The expression for Young's modulus is :

Options:

A) {{Mg\left( {{L_1} - L} \right)} \over {AL}}

B) {{MgL} \over {A{L_1}}}

C) {{MgL} \over {A\left( {{L_1} - L} \right)}}

D) {{Mg{L_1}} \over {AL}}

318

Medium

A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in tmperature. The length of aluminium rod is : ($\alpha Cu = 1.7 × 10–5 K–1 and \alpha $Al = 2.2 × 10–5 K–1)

Options:

A) 119.9 cm

B) 88 cm

C) 68 cm

D) 6.8 cm

319

Medium

When a block of mass M is suspended by a long wire of length L, the length of the wire becomes (L + $l$). The elastic potential energy stored in the extended wire is :

Options:

A) Mgl

B) mgL

C) {1 \over 2}$Mgl

D) {1 \over 2}$MgL

320

Medium

A small hole of area of cross-section 2 mm2 present near the bottom of a fully filled open tank of height 2 m. Taking g = 10 m/s2, the rate of flow of water through the open hole would be nearly :

Options:

A) 8.9 × 10–6 m3/s

B) 2.23 × 10–6 m3/s

C) 6.4 × 10–6 m3/s

D) 12.6 × 10–6 m3/s

321

Medium

The unit of thermal conductivity is :

Options:

A) J m–1 K–1

B) W m K–1

C) J m K–1

D) W m–1 K–1

322

Medium

A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2.5 $ \times $ 10–2 N/m. The pressure inside the bubble equals at a point Z0 below the free surface of water in a container. Taking g = 10 m/s2, density of water = 103 kg/m3, the value of Z0 is :

Options:

A) 1 cm

B) 10 cm

C) 100 cm

D) 0.5 cm

323

Medium

The power radiated by a black body is P and it radiates maximum energy at wavelength, $\lambda 0 . If the temperature of the black body is now changed so that it radiates maximum energy at wavelength {3 \over 4}{\lambda _0}$, the power radiated by it becomes nP. The value of n is

Options:

A) {3 \over 4}

B) {4 \over 3}

C) {{256} \over {81}}

D) {{81} \over {256}}

324

Medium

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by $\Delta $l on applying a force F, how much force is needed to stretch the second wire by the same amount?

Options:

A) 6F

B) F

C) 9F

D) 4F

325

Medium

A small sphere of radius ‘r’ falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to

Options:

A) r3

B) r2

C) r5

D) r4

326

Medium

A spherical black body with a radius of 12 cm radiates 450 watt power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watt would be

Options:

A) 450

B) 1000

C) 1800

D) 225

327

Medium

Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K1 and K2. The thermal conductivity of the composite will be

Options:

A) {{3\left( {{K_1} + {K_2}} \right)} \over 2}

B) {K_1} + {K_2}

C) 2\left( {{K_1} + {K_2}} \right)

D) {{{K_1} + {K_2}} \over 2}

328

Medium

A U tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water level on the other side. Meanwhile the water rises by 65 mm from its original level (see diagram). The density of the oil is

Options:

A) 425 kg m$-$3

B) 800 kg m$-$3

C) 928 kg m$-$3

D) 650 kg m$-$3

329

Medium

The bulk modulus of a spherical object is 'B'. If it is subjected to uniform pressure 'P', the fractional decrease in radius is

Options:

A) {B \over {3p}}

B) {{3p} \over B}

C) {p \over {3B}}

D) {p \over B}

330

Medium

A body cools from a temperature 3T to 2T in 10 minutes. The room temperature is T. Assume that Newton's law of cooling is applicable. The temperature of the body at the end of next 10 minutes will be

Options:

A) {7 \over 4}\,$ T

B) {3 \over 2}$ T

C) {4 \over 3}$ T

D) T

331

Medium

Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is at 100oC, while the other one is at 0oC. If the two bodies are brought into contact, then, assuming no heat loss, the final common temperature is

Options:

A) 50 oC

B) more than 50 oC

C) less than 50 oC but greater than 0 oC

D) 0 oC

332

Medium

A rectangular film of liquid is extended from (4 cm $ \times 2 cm) to (5 cm \times 4 cm). If the work done is 3 \times 10-$4 J, the value of the surface tension of the liquid is

Options:

A) 0.250 N m$-$1

B) 0.125 N m$-$1

C) 0.2 N m$-$1

D) 8.0 N m$-$1

333

Medium

Three liquids of densities $\rho 1, \rho 2 and \rho 3 (with \rho 1 > \rho 2 > \rho 3), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact \theta 1, \theta 2 and \theta $3 obey

Options:

A) {\pi \over 2} > {\theta _1} > {\theta _2} > {\theta _3} \ge 0

B) 0 $ \le \theta 1 < \theta 2 < \theta 3 < {\pi \over 2}

C) {\pi \over 2} < {\theta _1} < {\theta _2} < {\theta _3} < \pi

D) \pi > {\theta _1} > {\theta _2} > {\theta _3} > {\pi \over 2}

334

Medium

Coefficient of linear expansion of brass and steel rods are $\alpha 1 and \alpha 2. Lengths of brass and steel rods are l1 and l2 respectively. If (l1 - l$2) is maintained same at all temperatures, which one of the following relations holds good?

Options:

A) \alpha 1l2 = \alpha 2 2l$1

B) \alpha 1l1 = \alpha $2l2

C) \alpha 1l2 = \alpha 2l$1

D) \alpha 1l22 = \alpha 2l$12

335

Medium

A black body is at a temperature of 5760 K. The energy of radiation emitted by the body at wavelength 250 nm is U1, at wavelength 500 nm is U2 and that at 1000 nm is U3. Wien's constant, b = 2.88 $ \times $ 106 nm K. Which of the following is correct ?

Options:

A) U1 > U2

B) U2 > U1

C) U1 = 0

D) U3 = 0

336

Medium

A piece of ice falls from a height h so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of h [Latent heat of ice is $3.4 \times {10^5}$ J/kg and g = 10 N/Kg]

Options:

A) 136 km

B) 68 km

C) 34 km

D) 544 km

337

Medium

Two non-mixing liquids of densities $\rho and n\rho (n > 1) are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length \rho L (\rho $ < 1) in the denser liquid. The density d is equal to

Options:

A) \left\{ {2 + \left( {n - 1} \right)p} \right\}\rho

B) \left\{ {1 + \left( {n - 1} \right)p} \right\}\rho

C) \left\{ {1 + \left( {n + 1} \right)p} \right\}\rho

D) \left\{ {2 + \left( {n + 1} \right)p} \right\}\rho

338

Medium

The value of coefficient of volume expansion of glycerin is 5 $ \times 10-4 K-$1. The fractional change in the density of glycerin for a rise of 40oC in its temperature, is

Options:

A) 0.025

B) 0.010

C) 0.015

D) 0.020

339

Medium

The Young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of

Options:

A) 4 : 1

B) 1 : 1

C) 1 : 2

D) 2 : 1

340

Medium

Water rises to a height h in capillary tube. If the length of capillary tube above the surface of water is made less than h, then

Options:

A) water rises upto a point a little below the top and stays there.

B) water does not rise at all.

C) water rises upto the tip of capillary tube and then starts overflowing like a fountain.

D) water rises upto the top of capillary tube and stays there without overflowing.

341

Medium

The cylindrical tube of a spray pump has radius R, one end of which has n fine holes, each of radius r. If the speed of the liquid in the tube is V, the speed of the ejection of the liquid through the holes is

Options:

A) {{VR{}^2} \over {{n^3}{r^2}}}

B) {{{V^2}R} \over {nr}}

C) {{V{R^2}} \over {{n^2}{r^2}}}

D) {{V{R^2}} \over {n{r^2}}}

342

Medium

The approximate depth of an ocean is 2700 m. The compressiblity of water is 45.4 $ \times 10-11 Pa-$1 and density of water is 103 kg/m3. What fractional compression of water will be obtained at the bottom of the ocean?

Options:

A) 1.2 $ \times 10-$2

B) 1.4 $ \times 10-$2

C) 0.8 $ \times 10-$2

D) 1.0 $ \times 10-$2

343

Medium

On observing light from three different starts P, Q and R, it was found that intensity of violet colour is maximum in the spectrum of P, the intensity of green colour is maximum in the spectrum of R and the intensity of red colour is maximum in the spectrum of Q. If TP, TQ and TR are the respective absolute temperatures of P, Q and R, then it can be conclued from the above observations that

Options:

A) TP < TR < TQ

B) TP < TQ < TR

C) TP > TQ > TR

D) TP > TR > TQ

344

Medium

A wind with speed 40 m/s blows parallel to the roof of a house. The area of the roof is 250 m2. Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be $({\rho _{air}} = 1.2kg/{m^3})

Options:

A) 2.4 $ \times $ 105 N, upwards

B) 2.4 $ \times $ 105 N, downwards

C) 4.8 $ \times $ 105 N, downwards

D) 4.8 $ \times $ 105 N, upwards

345

Medium

The two ends of a metal rod are maintained at temperatures 100oC and 110oC. The rate of heat flow in the rod is found to be 4.0 J/s. If the ends are maintained at temperatures 200oC and 210oC, the rate of heat flow will be

Options:

A) 8.0 J/s

B) 4.0 J/s

C) 44.0 J/s

D) 16.8 J/s

346

Medium

A certain number of spherical drops of a liquid of radius r coalesce to form a single drop of radius R and volume V. If T is the surface tension of the liquid, then

Options:

A) energy = 4VT $\left( {{1 \over r} - {1 \over R}} \right)$ is released.

B) energy = 3VT$\left( {{1 \over r} + {1 \over R}} \right)$ is absorbed.

C) energy = 3VT$\left( {{1 \over r} - {1 \over R}} \right)$ is released

D) energy is neither released nor absorbed.

347

Medium

Steam at 100oC is passed into 20 g of water at 10oC. When water acquires a temperature of 80oC, the mass of water present will be [Take specific heat of water = 1 cal g$-1 oC-1 and latent heat of steam = 540 cal g-$1]

Options:

A) 24 g

B) 31.5 g

C) 42.5 g

D) 22.5 g

348

Medium

Certain quantity of water cools from 70oC to 60oC in the first 5 minutes and to 54oC in the next 5 minutes. The temperature of the surroundings is

Options:

A) 45oC

B) 20oC

C) 42oC

D) 10oC

349

Medium

Copper of fixed volume V is drawn into wire of length $l. When this wire is subjected to a constant force F, the extension produced in the wire is \Delta l$. Which of the following graphs is a straight line ?

Options:

A) \Delta l versus 1/l

B) \Delta l versus l$2

C) \Delta l versus 1/l$2

D) \Delta l versus l

350

Medium

Two metal rods 1 and 2 of same lengths have same temperature difference between their ends. Their thermal conductivities are K1 and K2 and cross sectional areas A1 and A2, respectively. If the rate of heat conduction in 1 is four times that in 2, then

Options:

A) K1A1 = 4K2A2

B) K1A1 = 2K2A2

C) 4K1A1 = K2A2

D) K1A1 = K2A2

351

Medium

If the ratio of diameters, lengths and Young's modulus of steel and copper wires shown in the figure are p, q and s respectively, then the corresponding ratio of increase in their lengths would be

Options:

A) \left( {{{5q} \over {7s{p^2}}}} \right)

B) \left( {{{7q} \over {5s{p^2}}}} \right)

C) \left( {{{2q} \over {5sp}}} \right)

D) \left( {{{7q} \over {5sp}}} \right)

352

Medium

A fluid is in streamline flow across a horizontal pipe of variable area of cross section. For this which of the following statements is correct?

Options:

A) The velocity is maximum at the narrowest part of the pipe and pressure is maximum at the widest part of the pipe.

B) Velocity and pressure both are maximum at the narrowest part of the pipe.

C) velocity and pressure both are maximum at the widest part of the pipe.

D) The velocity is minimum at the narrowest part of the pipe and the pressure is minimum at the widest part of the pipe.

353

Medium

The density of water at 20oC is 998 kg/m3 and at 40oC is 992 kg/m3. The coefficient of volume expansion of water is

Options:

A) 3 $ \times 10-$4/oC

B) 2 $ \times 10-$4/oC

C) 6 $ \times 10-$4/oC

D) 10 $ \times 10-$4/oC

354

Medium

A piece of iron is heated in a flame. It first becomes dull red then becomes reddish yellow and finally turns to white hot. The correct explanation for the above observation is possible by using

Options:

A) Kirchhoff's Law

B) Newton's Law of cooling

C) Stefan's Law

D) Wien's displacement Law

355

Medium

The molar specific heats of an ideal gas at constant pressure and volume are denoted by Cp and Cv, respectively. If $\gamma = {{{C_p}} \over {{C_v}}}$ and R is the universal gas constant, then Cv is equal to

Options:

A) {{\left( {\gamma - 1} \right)} \over R}

B) \gamma R

C) {{1 + \gamma } \over {1 - \gamma }}

D) {R \over {\left( {\gamma - 1} \right)}}

356

Medium

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?

Options:

A) length = 200 cm, diameter = 2 mm

B) length = 300 cm, diameter = 3 mm

C) length = 50 cm, diameter = 0.5 mm

D) length = 100 cm, diameter = 1 mm

357

Medium

The wettability of a surface by a liquid depends primarily on

Options:

A) density

B) angle of contact between the surface and the liquid

C) viscosity

D) surface tension

358

Medium

A slab of stone of area 0.36 m2 and thickness 0.1 m is exposed on the lower surface to steam at 100oC. A block of ice at 0oC rests on the upper surface of the slab. In one hour 4.8 kg of ice is melted. The thermal conductivity of slab is (Given latent heat of fusion of ice = 3.36 $ \times 105 J kg-$1)

Options:

A) 1.24 J/m/s/oC

B) 1.29 J/m/s/oC

C) 2.05 J/m/s/oC

D) 1.02 J/m/s/oC

359

Medium

If the radius of a star is R and it acts as a black body, what would be the temperature of the star, in which the rate of energy production is Q?

Options:

A) {Q \over {4\pi {R^2}\sigma }}

B) {\left( {{Q \over {4\pi {R^2}\sigma }}} \right)^{ - 1/2}}

C) {\left( {{{4\pi {R^2}Q} \over \sigma }} \right)^{1/4}}

D) {\left( {{Q \over {4\pi {R^2}\sigma }}} \right)^{1/4}}

360

Medium

Liquid oxygen at 50 K is heated to 300 K at constant pressure of 1 atm. The rate of heating is constant. Which one of the following graphs represents the variation of temperature with time ?

Options:

361

Medium

Assuming the sun to have a spherical outer surface of radius r, radiating like a black body at temperature toC, the power received by a unit surface, (normal to the incident rays) at a distance R from the centre of the sun is where $\sigma $ is the Stefan's constant.

Options:

A) {{{r^2}\sigma {{\left( {t + 273} \right)}^4}} \over {4\pi {R^2}}}

B) {{16{\pi ^2}{r^2}\sigma {t^4}} \over {{R^2}}}

C) {{{r^2}\sigma {{\left( {t + 273} \right)}^4}} \over {{R^2}}}

D) {{4\pi {r^2}\sigma {t^4}} \over {{R^2}}}

362

Medium

The total radiant energy per unit area, normal to the direction of incidence, received at a distance R from the centre of a star of radius r, whose outer surface radiates as a black body at a temperature TK is given by

Options:

A) {{\sigma {r^2}{T^4}} \over {{R^2}}}

B) {{\sigma {r^2}{T^4}} \over {4\pi {R^2}}}

C) {{\sigma {r^2}{T^4}} \over {{R^4}}}

D) {{4\pi \sigma {r^2}{T^4}} \over {{R^2}}}

363

Medium

A cylindrical metallic rod in thermal contact with two reservoirs of heat at its two ends conducts an amount of heat Q in time t. The metallic rod is melted and the material is formed into a rod of half the radius of the original rod. What is the amount of heat conducted by the new rod, when placed in thermal contact with the two reservoirs in time t?

Options:

A) {Q \over 4}

B) {Q \over {16}}

C) 2Q

D) {Q \over 2}

364

Medium

The two ends of a rod of length L and a uniform cross-sectional area A are Kept at two temperatures T1 and T2 (T1 > T2). The rate of heat transfer, ${{dQ} \over {dt}}$ through the rod in a steady state is given by :

Options:

A) {{dQ} \over {dt}} = {{k\left( {{T_1} - {T_2}} \right)} \over {LA}}

B) {{dQ} \over {dt}} = kLA({T_1} - {T_2})

C) {{dQ} \over {dt}} = {{kA\left( {{T_1} - {T_2}} \right)} \over L}

D) {{dQ} \over {dt}} = {{kL\left( {{T_1} - {T_2}} \right)} \over A}

365

Medium

A black body at 227oC radiates heat at the rate of 7 cals/cm2s. At a temperature of 727oC, the rate of heat radiated in the same units will be

Options:

A) 50

B) 112

C) 80

D) 60

366

Medium

On a new scale of temperature (which is linear) and called the W scale, the freezing and boiling points of water are 39oW and 239oW respectively. What will be the temperature on the new scale, corresponding to a temperature of 39oC on the Celsius scale ?

Options:

A) 200oW

B) 139oW

C) 78oW

D) 117oW

367

Medium

A black body is at 727oC. It emits energy at a rate which is proportional to

Options:

A) (1000)4

B) (1000)2

C) (727)4

D) (727)2

368

Medium

Assuming the sun to have a spherical outer surface of radius r, radiating like a black body at temperature toC, the power received by a unit surface, (normal to the incident rays) at a distance R from the centre of the sun is where $\sigma $ is the Stefan's constant.

Options:

A) {{{r^2}\sigma {{\left( {t + 273} \right)}^4}} \over {4\pi {R^2}}}

B) {{16{\pi ^2}{r^2}\sigma {t^4}} \over {{R^2}}}

C) {{{r^2}\sigma {{\left( {t + 273} \right)}^4}} \over {{R^2}}}

D) {{4\pi {r^2}\sigma {t^4}} \over {{R^2}}}

369

Medium

A black body at 1227oC emits radiations with maximum intensity at a wavelength of 5000 $\mathop A\limits^ \circ $. If the temperature of the body is increased by 1000oC, the maximum intensity will be observed at

Options:

A) 3000 $\mathop A\limits^ \circ

B) 4000$\mathop A\limits^ \circ

C) 5000$\mathop A\limits^ \circ

D) 6000$\mathop A\limits^ \circ

370

Medium

Which of the following rods, (given radius r and length $l$) each made of the same material and whose ends are maintained at the same temperature will conduct most heat ?

Options:

A) r = r0, $l = l$0

B) r = 2r0, $l = l$0

C) r = r0, $l = 2l$0

D) r = 2r0, $l = 2l$0

371

Medium

If $\lambda $m denotes the wavelength at which the radioactive amission from a black body at a temperature TK is maximum, then

Options:

A) {\lambda _m}\, \propto \,{T^4}

B) {\lambda _m}$ is independent of T

C) {\lambda _m} \propto $ T

D) {\lambda _m}\, \propto \,{T^{ - 1}}

372

Medium

Consider a compound slab consisting of two different materials having equal thicknesses and thermal conductivities K and 2K, respectively. The equivalent thermal conductivity of the slab is

Options:

A) {2 \over 3}K

B) \sqrt 2 K

C) 3 K

D) {4 \over 3}K

373

Medium

The Wien's displacement law express relation between

Options:

A) wavelength corresponding to maximum energy and temperature

B) radiation energy and wavelength

C) temperature and wavelength

D) colour of light and temperature.

374

Medium

Which of the following is best close to an ideal black body?

Options:

A) black lamp

B) cavity maintained at constant temperature

C) platinium black

D) a lump of charcoal heated to high temperature.

375

Medium

Consider two rods of same length and different specific heats (S1, S2), conductivities (K1, K2) and area of cross-sections (A1, A2) and both having temperatures T1 and T2 at their ends. If rate of loss of heat due to conduction is equal, then

Options:

A) K1A1 = K2A2

B) {{{K_1}{A_1}} \over {{S_1}}} = {{{K_2}{A_2}} \over {{S_2}}}

C) K2A1 = K1A2

D) {{{K_2}{A_1}} \over {{S_2}}} = {{{K_1}{A_2}} \over {{S_1}}}

376

Medium

For a black body at temperature 727oC, its radiating power is 60 watt and temperature of surrounding is 227oC. If temperature of black body is changed to 1227oC then its radiating power will be

Options:

A) 304 W

B) 320 W

C) 240 W

D) 120 W

377

Medium

Unit of Stefan's constant is

Options:

A) watt m2 K4

B) watt m2/K4

C) watt/m2 K

D) watt/m2K4

378

Medium

A cylindrical rod having temperature T1 and T2 at its end. The rate of flow of heat Q1 cal/sec. If all the linear dimension are doubled keeping temperature constant, then rate of flow of heat Q2 will be

Options:

A) 4Q1

B) 2Q1

C) {{{Q_1}} \over 4}

D) {{{Q_1}} \over 2}

379

Medium

A black body has maximum wavelength $\lambda $m at 2000 K. Its corresponding wavelength at 3000 K will be

Options:

A) {3 \over 2}{\lambda _m}

B) {2 \over 3}{\lambda _m}

C) {{16} \over {81}}{\lambda _m}

D) {{81} \over {16}}{\lambda _m}

379

Total Questions

109

Easy

269

Medium

Hard

Study Tips

Before You Start

• Review the chapter concepts thoroughly
• Keep a notebook for important formulas
• Practice similar problems from your textbook
• Time yourself to improve speed

After Practice

• Review all incorrect answers carefully
• Watch video solutions for difficult questions
• Make notes of common mistakes
• Practice similar questions again later