Question 115: Units , Dimensions and Error Analysis

Question

Match List I with List II :

List I (Physical Quantity)

List II (Dimensional Formula)

A.
Pressure gradient
I.
$$\left[\mathrm{M}^{\circ} \mathrm{L}^{2} \mathrm{~T}^{-2}\right]$$

B.
Energy density
II.
$$\left[\mathrm{M}^{1} \mathrm{L}^{-1} \mathrm{~T}^{-2}\right]$$

C.
Electric Field
III.
$$\left[\mathrm{M}^{1} \mathrm{L}^{-2} \mathrm{~T}^{-2}\right]$$

D.
Latent heat
IV.
$$\left[\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]$$

Choose the correct answer from the options given below:

Accepted Answer

Pressure gradient $=\frac{d p}{d x}=\frac{\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}ight]}{[\mathrm{L}]}$
$$
=\left[\mathrm{M}^{1} \mathrm{~L}^{-2} \mathrm{~T}^{-2}ight]
$$
Energy density $=\frac{	ext { energy }}{	ext { volume }}=\frac{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}ight]}{\left[\mathrm{L}^{3}ight]}$
$$
=\left[\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{-2}ight]
$$
Electric field $=\frac{	ext { Force }}{	ext { ch arge }}=\frac{\left[	ext { MLT }^{-2}ight]}{[	ext { A.T }]}$
$=\left[\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-3} \mathrm{~A}^{-1}ight]$
Latent heat $=\frac{	ext { heat }}{	ext { mass }}=\frac{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}ight]}{[\mathrm{M}]}$
$=\left[\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{-2}ight]$

Answer

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

Answer

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

Answer

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

Answer

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

Units , Dimensions and Error Analysis

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