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 0 L 2 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 dimensions of mass, length, time, temperature and current are M , L , T , K and I respectively)

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 0 L 2 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 dimensions of mass, length, time, temperature and current are M , L , T , K and I respectively), ( A ) ( B ) ( C ) ( D IV I III I, ( A ) ( B ) ( C ) ( D I IV II III, ( A ) ( B ) ( C ) ( D III II I IV, ( A ) ( B ) ( C ) ( D II III IV I

MARKS App · Accepted Answer

Gravitational Potential = Gravitational Potential Energy mass = ML 2 T - 2 M = M 0 L 2 T - 2 Stefan's constant σ . d Q d t = σ A T 4 ⇒ σ = d Q d t A T 4 ⇒ σ = ML 2 T - 3 L 2 K 4 = ML 0 T - 3 K - 4 Permittivity ε 0 F = 1 4 π ε 0 q 2 r 2 ∴ ε 0 = 1 4 π F q 2 r 2 = I 2 T 2 MLT - 2 · L 2 = M - 1 L - 3 T 4 I 2 Specific heat capacity C Q = m C ∆ T ⇒ C = Q m ∆ T = ML 2 T - 2 M · K = M 0 L 2 T - 2 K - 1

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List - I			List - II
A	Gravitational potential	I	$M^{0} L^{2} T^{- 2} K^{- 1}$
B	Stefan's constant	II	$M^{0} L^{2} T^{- 2}$
C	Permittivity	III	${ML}^{0} T^{- 3} K^{- 4}$
D	Specific heat capacity	IV	$M^{- 1} L^{- 3} T^{4} I^{2}$