Match List-I with List-II. Boltzmann constant [2026]

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Solution

Q.
Match List-I with List-II. [2026]

List-I List-II

A. Boltzmann constant I. $[M^{- 1} L^{3} T^{- 2}]$

B. Stefan’s constant II. $[M L^{2} T^{- 1}]$

C. Planck’s constant III. $[M L^{2} T^{- 2} K^{- 1}]$

D. Gravitational constant IV. $[M L^{0} T^{- 3} K^{- 4}]$

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

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

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

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

Ans.
(3)

$Boltzmann constant = \frac{Energy}{Temp.}$

$\Rightarrow [k] = [M L^{2} T^{- 2} K^{- 1}]$

$σ \Rightarrow \frac{P}{A T^{4}} \Rightarrow [σ] = [M^{1} T^{- 3} K^{- 4}]$

$h = \frac{E}{ν} = E \cdot t \Rightarrow [h] = [M^{1} L^{2} T^{- 1}]$

$G = \frac{F r^{2}}{m^{2}} \Rightarrow [G] = [M^{- 1} L^{3} T^{- 2}]$

$Option (3) is correct.$

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