JEE Main 2025 Apr 3 Shift 2, Physics Q16: Units And Dimensions

JEE Main2025Apr 3, Shift 2Physics

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. Boltzmann constant	I. ML $^{2}$ T $^{- 1}$
B. Coefficient of viscosity	II. MLT $^{- 3}$ K $^{- 1}$
C. Planck's constant	III. ML $^{2}$ T $^{- 2}$ K $^{- 1}$
D. Thermal conductivity	IV. ML $^{- 1}$ T $^{- 1}$

Choose the correct answer from the options given below :

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

Solution

Derive each dimension from a defining relation.

(A) Boltzmann constant: $P V = N k T \Rightarrow [k] = \frac{[ P V ]}{[ T ]} = \frac{M L ^{2} T ^{- 2}}{K} = M L^{2} T^{- 2} K^{- 1}$ (III).

(B) Viscosity: from Stokes' law $F = 6 π η r v$ , $[η] = \frac{M L T ^{- 2}}{L \cdot L T ^{- 1}} = M L^{- 1} T^{- 1}$ (IV).

(D) Thermal conductivity: from $\frac{d Q}{d t} = k A \frac{d T}{d x}$ , $[k] = \frac{M L ^{2} T ^{- 3} \cdot L}{L ^{2} \cdot K} = M L T^{- 3} K^{- 1}$ (II).

$∴$ A-III, B-IV, C-I, D-II.

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JEE Main 2025 Apr 3 Shift 2, Physics Q16: Units And Dimensions

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