Units & Dimensions

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19 of 149

Question 19 of 149

Match List - I with List - II.List - IList - IIA. Boltzmann constantI. [M−1L3T−2][M^{-1}L^3T^{-2}]B. Stefan's constantII. [ML2T−1][ML^2T^{-1}]C. Planck's constantIII. [ML2T−2K−1][ML^2T^{-2}K^{-1}]D. Gravitational constantIV. [ML0T−3K−4][ML^0T^{-3}K^{-4}]Choose the correct answer from the options given below :

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Answer: (C) A-III, B-IV, C-II, D-I

Boltzmann constant kk: E=kT⇒[k]=[ML2T−2][K]=[ML2T−2K−1]E = k T \Rightarrow [k] = \dfrac{[ML^2T^{-2}]}{[K]} = [ML^2T^{-2}K^{-1}]

Stefan's constant σ\sigma: EAt=σT4⇒[σ]=[ML2T−2][L2][T][K4]=[ML0T−3K−4]\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 hh: E=hν⇒[h]=[ML2T−2][T−1]=[ML2T−1]E = h\nu \Rightarrow [h] = \dfrac{[ML^2T^{-2}]}{[T^{-1}]} = [ML^2T^{-1}]

Gravitational constant GG: F=Gm1m2r2⇒[G]=[MLT−2][L2][M2]=[M−1L3T−2]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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