Question

Match the physical quantities given in List-I with dimensions in List-II.

List I		List II
A.	Gravitational potential	(i)	$\left[ M ^{0} L ^{2} T ^{-2} K ^{-1}\right]$
B.	Stefan’s constant	(ii)	$\left[ M ^{-1} L ^{3} T ^{-2}\right]$
C.	Permittivity	(iii)	$\left[ ML ^{0} T ^{-3} K ^{-4}\right]$
D.	Specific heat capacity	(iv)	$\left[ M ^{-1} L^{-3} T ^{4} I ^{2}\right]$

(The dimension of mass, length, time, temperature and current are $M, L , T , K$ and $I$, respectively $) .$ The correct match is

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

Answer 1

Answer: (D)

Dimensions of the given physical quantities are as follows:
(A) Gravitational potential,
$\left[ m ^{3} / kg - s ^{-2}\right]=\left[ M ^{-1} L ^{3} T ^{-2}\right]$
(B) Stefan's constant,
$\left( W / m ^{2} K ^{4}\right)=\left[ ML ^{0} T ^{-3} K ^{4}\right]$
(C) Permittivity
$\left( C ^{2} / m ^{3} kgs ^{2}\right)=\left[ M ^{-1} L ^{-3} T ^{4} I ^{2}\right]$
(D) Specific heat capacity,
$\left( J / Kg ^{\circ} C \right)=\left[ M ^{0} L ^{2} T ^{-2} K ^{-1}\right]$
So, the correct sequence of match is
$A \rightarrow II , B \rightarrow III , C \rightarrow IV$ and $D \rightarrow I$