JEE Main · 2025 · 03 Apr 2025 · Shift 1 · Chapter_pending

The gravitational constant follows from $G=\frac{F{r}^2}{m_1{m}_2}$, giving dimensions $[M^{-1}{L}^3{T}^{-2}]$. Gravitational potential energy, of the form $mgh$, has dimensions $[M{L}^2{T}^{-2}]$. Gravitational potential is energy per unit mass, $[L^2{T}^{-2}]$. Acceleration due to gravity has dimensions $[L{T}^{-2}]$. Hence the gravitational constant matches $[M^{-1}{L}^3{T}^{-2}]$, the potential energy matches $[M{L}^2{T}^{-2}]$, the potential matches $[L^2{T}^{-2}]$, and the acceleration due to gravity matches $[L{T}^{-2}]$.