Physics - Unit & Dimension Question with Solution | TestHub

Let [Y] = [V] ${}^a[\mathrm{F}{]}^{\mathrm{b}}[\mathrm{A}{]}^{\mathrm{c}}$ $\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-2}\right]={\left[{\mathrm{LT}}^{-1}\right]}^{\mathrm{a}}{\left[{\mathrm{MLT}}^{-2}\right]}^{\mathrm{b}}{\left[{\mathrm{LT}}^{-2}\right]}^{\mathrm{c}}$ $\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-2}\right]=\left[{\mathrm{M}}^b{\mathrm{L}}^{\mathrm{a}+b+\mathrm{c}}{\mathrm{T}}^{-\mathrm{a}-2\mathrm{b}-2\mathrm{c}}\right]$ Comparing power both side of similar terms we get, $b=1,a+b+c=-1,-a-2b-2c=-2$ solving above equations we get $a=-4,b=1,c=2$ so $[\mathrm{Y}]=\left[{\mathrm{V}}^{-4}{\mathrm{FA}}^2\right]=\left[{\mathrm{V}}^{-4}{\mathrm{A}}^2\mathrm{F}\right]$