Q 11-01-187JEE MainJEE Main 2021 (26 Aug, Shift 1)Medium
If $E$, $L$, $M$ and $G$ denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of $P$ in the formula $P = EL^2M^{-5}G^{-2}$ are:
Answer: (D) $[\text{M}^0\text{L}^0\text{T}^0]$
$[E] = \text{ML}^2\text{T}^{-2}$, $[L] = \text{ML}^2\text{T}^{-1}$, $[G] = \text{M}^{-1}\text{L}^3\text{T}^{-2}$.
$$[P] = (\text{ML}^2\text{T}^{-2})(\text{M}^2\text{L}^4\text{T}^{-2})(\text{M}^{-5})(\text{M}^2\text{L}^{-6}\text{T}^4) = [\text{M}^0\text{L}^0\text{T}^0]$$
Solution by Sreeraj P, M.Sc Physics