Physics - Unit & Dimension Question with Solution | TestHub

$\begin{array}{rl}& \text{ (A) }\mathrm{G}=\frac{{\mathrm{Fr}}^2}{{\mathrm{m}}^2}\\ & [\mathrm{G}]=\frac{\left[{\mathrm{MLT}}^{-2}\right]\left[{\mathrm{L}}^2\right]}{\left[{\mathrm{M}}^2\right]}=\left[{\mathrm{M}}^{-1}{\mathrm{L}}^3{\mathrm{T}}^{-2}\right](\mathrm{IV})\end{array}$
(B)
$\begin{array}{rl}& \text{ P.E. }=\mathrm{mgh}=\left[{\mathrm{MLT}}^{-2}\mathrm{L}\right]\\ & =\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]\text{ (III) }\end{array}$
(C) Gravitational Potential $=\frac{\mathrm{GM}}{\mathrm{r}}$
$=\frac{\left[{\mathrm{M}}^{-1}{\mathrm{L}}^3{\mathrm{T}}^{-2}\right][\mathrm{M}]}{[\mathrm{L}]}=\left[{\mathrm{M}}^0{\mathrm{L}}^2{\mathrm{T}}^{-2}\right]=\left[{\mathrm{L}}^2{\mathrm{T}}^{-2}\right](\mathrm{II})$
(D) Acceleration due to gravity $=[\mathrm{g}]=\left[{\mathrm{LT}}^{-2}\right](\mathrm{I})$