Q 11-01-025JEE MainEAMCET 2008 (Engineering)Top questionHard
Energy ($E$), angular momentum ($L$) and the universal gravitational constant ($G$) are chosen as fundamental quantities. The power of $G$ in the dimensional formula of Planck's constant ($h$) is
Answer: (A) $0$
Planck's constant has dimensions $[ML^2T^{-1}]$, which are exactly the dimensions of angular momentum (for example, $L = nh/2\pi$ in Bohr's model).
So $h = E^0\,L^1\,G^0$, and the power of $G$ is $0$.
You can confirm by writing $[ML^2T^{-1}] = [ML^2T^{-2}]^a[ML^2T^{-1}]^b[M^{-1}L^3T^{-2}]^c$ and solving: $a = 0$, $b = 1$, $c = 0$.
Solution by Sreeraj P, M.Sc Physics