Physics - Unit & Dimension Question with Solution | TestHub

We know that, $F=\frac{G{M}_1{M}_2}{r^2}$ $\begin{array}{rl}& \Rightarrow [G]=\frac{[F]\left[r^2\right]}{\left[M_1\right]\left[M_2\right]}=\frac{\left[{\mathrm{MLT}}^{-2}\right]\left[{\mathrm{L}}^2\right]}{[\mathrm{M}][\mathrm{M}]}\\ & \Rightarrow [G]=\left[{\mathrm{M}}^{-1}{\mathrm{L}}^3{\mathrm{T}}^{-2}\right]\end{array}$ i.e., gravitational constant is mechanical quantity which has dimensions of reciprocal of mass $\left({\mathrm{M}}^{-1}\right)$