Match List - I with List - II.
$$\begin{array}{|l|l|l|l|}\hline & \text{List - I} & & \text{List - II} \\ \hline \text{A.} & \text{Boltzmann constant} & \text{I.} & [\text{M}^{-1}\text{L}^3\text{T}^{-2}] \\ \hline \text{B.} & \text{Stefan's constant} & \text{II.} & [\text{ML}^2\text{T}^{-1}] \\ \hline \text{C.} & \text{Planck's constant} & \text{III.} & [\text{ML}^2\text{T}^{-2}\text{K}^{-1}] \\ \hline \text{D.} & \text{Gravitational constant} & \text{IV.} & [\text{ML}^0\text{T}^{-3}\text{K}^{-4}] \\ \hline \end{array}$$
Choose the correct answer from the options given below :
Answer: (C) A-III, B-IV, C-II, D-I
- Boltzmann constant: $k = \dfrac{E}{T}$ → $\text{ML}^2\text{T}^{-2}\text{K}^{-1}$ (III).
- Stefan's constant: $\sigma = \dfrac{P/A}{T^4}$ → $\dfrac{\text{MT}^{-3}}{\text{K}^4}$ = $\text{ML}^0\text{T}^{-3}\text{K}^{-4}$ (IV).
- Planck's constant: $h = \dfrac{E}{\nu}$ → $\text{ML}^2\text{T}^{-1}$ (II).
- Gravitational constant: $G = \dfrac{Fr^2}{m^2}$ → $\text{M}^{-1}\text{L}^3\text{T}^{-2}$ (I).
So A-III, B-IV, C-II, D-I.
Solution by Sreeraj P, M.Sc Physics