Q52 / 75 · JEE Main 2026 (06 April Shift 2) · Physics
Match List - I with List - II.List - I List - II A. Boltzmann constant I. $[M^{-1}L^3T^{-2}]$ B. Stefan's constant II. $[ML^2T^{-1}]$ C. Planck's constant III. $[ML^2T^{-2}K^{-1}]$ D. Gravitational constant IV. $[ML^0T^{-3}K^{-4}]$
Choose the correct answer from the options given below :
| List - I | List - II |
|---|---|
| A. Boltzmann constant | I. $[M^{-1}L^3T^{-2}]$ |
| B. Stefan's constant | II. $[ML^2T^{-1}]$ |
| C. Planck's constant | III. $[ML^2T^{-2}K^{-1}]$ |
| D. Gravitational constant | IV. $[ML^0T^{-3}K^{-4}]$ |
- AA-I, B-II, C-III, D-IV
- BA-IV, B-III, C-II, D-I
- Correct answerCA-III, B-IV, C-II, D-I
- DA-II, B-I, C-IV, D-III
Solution
Boltzmann constant $k$: $E = k T \Rightarrow [k] = \dfrac{[ML^2T^{-2}]}{[K]} = [ML^2T^{-2}K^{-1}]$
Stefan's constant $\sigma$: $\dfrac{E}{At} = \sigma T^4 \Rightarrow [\sigma] = \dfrac{[ML^2T^{-2}]}{[L^2][T][K^4]} = [ML^0T^{-3}K^{-4}]$
Planck's constant $h$: $E = h\nu \Rightarrow [h] = \dfrac{[ML^2T^{-2}]}{[T^{-1}]} = [ML^2T^{-1}]$
Gravitational constant $G$: $F = \dfrac{Gm_1m_2}{r^2} \Rightarrow [G] = \dfrac{[MLT^{-2}][L^2]}{[M^2]} = [M^{-1}L^3T^{-2}]$
Thus, A-III, B-IV, C-II, D-I.
Answer: A-III, B-IV, C-II, D-I
Stefan's constant $\sigma$: $\dfrac{E}{At} = \sigma T^4 \Rightarrow [\sigma] = \dfrac{[ML^2T^{-2}]}{[L^2][T][K^4]} = [ML^0T^{-3}K^{-4}]$
Planck's constant $h$: $E = h\nu \Rightarrow [h] = \dfrac{[ML^2T^{-2}]}{[T^{-1}]} = [ML^2T^{-1}]$
Gravitational constant $G$: $F = \dfrac{Gm_1m_2}{r^2} \Rightarrow [G] = \dfrac{[MLT^{-2}][L^2]}{[M^2]} = [M^{-1}L^3T^{-2}]$
Thus, A-III, B-IV, C-II, D-I.
Answer: A-III, B-IV, C-II, D-I
Hence, the correct answer is option: 'C'.