Match the physical quantities given in List-I with dimensions in List-II. List I List II A. Gravitational potential (i) [ M 0 L 2 T -2 K -1] B. Stefan’s constant (ii) [ M -1 L 3 T -2] C. Permittivity (iii) [ ML 0 T -3 K -4] D. Specific heat capacity (iv) [ M -1 L-3 T 4 I 2] (The dimension of mass, length, time, temperature and current are M, L , T , K and I, respectively ) . The correct match is

Question

Match the physical quantities given in List-I with dimensions in List-II. List I List II A. Gravitational potential (i) [ M 0 L 2 T -2 K -1] B. Stefan’s constant (ii) [ M -1 L 3 T -2] C. Permittivity (iii) [ ML 0 T -3 K -4] D. Specific heat capacity (iv) [ M -1 L-3 T 4 I 2] (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)

Tardigrade Admin · Accepted Answer

Dimensions of the given physical quantities are as follows:
(A) Gravitational potential,

[m^{3} / k g - s^{- 2}] = [M^{- 1} L^{3} T^{- 2}]

(B) Stefan's constant,

(W / m^{2} K^{4}) = [M L^{0} T^{- 3} K^{4}]

(C) Permittivity

(C^{2} / m^{3} k g s^{2}) = [M^{- 1} L^{- 3} T^{4} I^{2}]

(D) Specific heat capacity,

(J / K g^{\circ} C) = [M^{0} L^{2} T^{- 2} K^{- 1}]

So, the correct sequence of match is

A \to II, B \to III, C \to I V

and

D \to I

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