Match List - I with List - II, where $h$, $G$ and $c$ are taken as fundamental units.
$$\begin{array}{|l|l|l|l|}\hline & \text{List - I} & & \text{List - II} \\ \hline \text{A.} & \text{Meter (L)} & \text{I.} & \sqrt{\dfrac{hc}{G}} \\ \hline \text{B.} & \text{Second (S)} & \text{II.} & \sqrt{\dfrac{Gh}{c^5}} \\ \hline \text{C.} & \text{Kilogram (M)} & \text{III.} & \sqrt{\dfrac{K^2L^2c^3}{Gh}} \\ \hline \text{D.} & \text{Kelvin (K)} & \text{IV.} & \sqrt{\dfrac{Gh}{c^3}} \\ \hline \end{array}$$
Choose the correct answer from the options given below :
Answer: (B) A-IV, B-II, C-I, D-III
These are the Planck units built from $h$, $G$ and $c$:
- Length: $\sqrt{\dfrac{Gh}{c^3}}$ (IV).
- Time: length$/c$ $= \sqrt{\dfrac{Gh}{c^5}}$ (II).
- Mass: $\sqrt{\dfrac{hc}{G}}$ (I).
- Temperature: the remaining expression (III), which brings in the Boltzmann constant.
So A-IV, B-II, C-I, D-III.
Solution by Sreeraj P, M.Sc Physics