Physics - Unit & Dimension Question with Solution | TestHub

Let$F\propto P^x{V}^y{T}^z$

by substituting the following dimensions :

$\left[P\right]=\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-2}\right], \left[V\right]=\left[{\mathrm{LT}}^{-1}\right],\mathrm{ }\left[T\right]=\left[\mathrm{T}\right]$

and comparing the dimension of both sides

$x=1,\mathrm{ }y=2,\mathrm{ }z=2$$F=P{V}^2{T}^2$