JEE Mains · Physics · STD 11 - Units,dimensions and measurement
- JEE Mains 2026
- Medium
- MCQ
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. \([ML^0T^{-3}K^{-4}]\) |
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) A-III, B-IV, C-II, D-I
Step-by-step Solution
Detailed explanation
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
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