Question

Match List I with List II:

List I (Physical Quantity)		List II (Dimensional Formula)
A	Pressure gradient	I	$\left[ M ^{\circ} L ^2 T ^{-2}\right]$
B	Energy density	II	$\left[ M ^1 L ^{-1} T ^{-2}\right]$
C	Electric Field	III	$\left[ M ^1 L ^{-2} T ^{-2}\right]$
D	Latent heat	IV	$\left[ M ^1 L ^1 T ^{-3} A ^{-1}\right]$

Choose the correct answer from the options given below:

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

Answer 1

Answer: (B)

Pressure gradient $=\frac{ dp }{ dx }=\frac{\left[ ML ^{-1} T ^{-2}\right]}{[ L ]} $
$ =\left[ M ^1 L ^{-2} T ^{-2}\right] $
Energy density $=\frac{\text { energy }}{\text { volume }}=\frac{\left[ ML ^2 T ^{-2}\right]}{\left[ L ^3\right]} $
$ =\left[ M ^1 L ^{-1} T ^{-2}\right] $
Electric field $=\frac{\text { Force }}{\text { ch arge }}=\frac{\left[ MLT ^{-2}\right]}{[\text { A.T }]} $
$ =\left[ M ^1 L ^1 T ^{-3} A ^{-1}\right] $
Latent heat $=\frac{\text { heat }}{\text { mass }}=\frac{\left[ ML ^2 T ^{-2}\right]}{[ M ]} $
$ =\left[ M ^0 L ^2 T ^{-2}\right] $