Q 11-01-096JEE MainJEE Main 2024 (5 Apr, Shift 1)Medium
If $G$ is the gravitational constant and $u$ is the energy density, then which of the following quantities has the same dimensions as $\sqrt{uG}$?
Answer: (D) force per unit mass
$[u] = [\text{M}\text{L}^{-1}\text{T}^{-2}]$ and $[G] = [\text{M}^{-1}\text{L}^3\text{T}^{-2}]$.
$$[uG] = [\text{L}^2\text{T}^{-4}] \Rightarrow \left[\sqrt{uG}\right] = [\text{L}\text{T}^{-2}]$$
This is acceleration, i.e. force per unit mass.
Solution by Sreeraj P, M.Sc Physics