Physics - Unit & Dimension Question with Solution | TestHub

$\mathrm{d}\propto F^{\mathrm{a}}{\mathrm{L}}^{\mathrm{b}}{\mathrm{T}}^{\mathrm{c}}$

$\left[M{L}^{-3}\right]={\left[ML{T}^{-2}\right]}^a\left[L^b\right]\left[T{ }^c\right]$

$=\left[M^a{L}^{a+b}{T}^{-2a+c}\right]$

comparing :

$a=1$ ......(i)

$a+b=-3$ ....(ii)

$-2 a+c=0$ .......(iii)

$\mathrm{c}=2 ; \mathrm{b}=-4 ; \therefore \left[\mathrm{d}\right]=\left[{\mathrm{FL}}^{-4}{ \mathrm{T}}^2\right]$