Physics - Unit & Dimension Question with Solution | TestHub

Let $[G]\propto c^x{g}^y{p}^z$

by substituting the following dimensions :

$$\begin{gathered} \left[\mathrm{G}\right]=\left[{\mathrm{M}}^{-1}{\mathrm{L}}^3{\mathrm{T}}^{-2}\right], \\ \left[\mathrm{c}\right]=\left[{\mathrm{LT}}^{-1}\right], \\ \left[\mathrm{g}\right]=\left[{\mathrm{LT}}^{-2}\right] \end{gathered}$$

$\left[\mathrm{p}\right]=\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-2}\right]$

and by comparing the powers of both sides we can get $x=0,y=2,z=-1$
∴ $[G]\propto c^0{g}^2{p}^{-1}$