Question 33: Units , Dimensions and Error Analysis

Question

Match
List - I
with
List - II
.
List - I
List - II
(A) Mass density
(I) [ML
2
T
−3
]
(B) Impulse
(II) [MLT
−1
]
(C) Power
(III) [ML
2
T
0
]
(D) Moment of inertia
(IV) [ML
−3
T
0
]
Choose the
correct
answer from the options given below :

Accepted Answer

(A) Mass density:
Mass density is defined as mass per unit volume.
The dimension of mass is $$[M]$$.
The dimension of volume is $$[L^3]$$.
Therefore, the dimension of mass density is $$\frac{[M]}{[L^3]} = [ML^{-3}T^{0}]$$.
Matches with (IV).
(B) Impulse:
Impulse is defined as the change in momentum, or force multiplied by time.
Impulse = Force x Time
The dimension of force is $$[MLT^{-2}]$$.
The dimension of time is $$[T]$$.
Therefore, the dimension of impulse is $$[MLT^{-2}] \cdot [T] = [MLT^{-1}]$$.
Matches with (II).
(C) Power:
Power is defined as the rate of doing work or energy per unit time.
Power = Work / Time
The dimension of work (or energy) is $$[ML^2T^{-2}]$$.
The dimension of time is $$[T]$$.
Therefore, the dimension of power is $$\frac{[ML^2T^{-2}]}{[T]} = [ML^2T^{-3}]$$.
Matches with (I).
(D) Moment of inertia:
Moment of inertia is defined as $$I = mr^2$$, where m is mass and r is the distance from the axis of rotation.
The dimension of mass is $$[M]$$.
The dimension of distance squared is $$[L^2]$$.
Therefore, the dimension of moment of inertia is $$[ML^2T^{0}]$$.
Matches with (III).
So, the correct matches are:
(A) - (IV)
(B) - (II)
(C) - (I)
(D) - (III)
Therefore, the correct option is
D
.

Answer

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

Answer

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

Answer

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

Answer

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

Units , Dimensions and Error Analysis

Match List - I with List - II . List - I List - II (A) Mass density (I) [ML 2 T −3 ] (B) Impulse (II) [MLT −1 ] (C) Power (III) [ML 2 T 0 ] (D) Moment of inertia (IV) [ML −3 T 0 ] Choose the correct answer from the options given below :

Choose the correct answer: