Physics - Unit & Dimension Question with Solution | TestHub

Let$Y=f\left(V, F, A\right)$

$Y=K{V}^x{F}^y{A}^z, K\to$Unit less

$\left[Y\right]={\left[V\right]}^x{\left[F\right]}^y{\left[A\right]}^z$

$\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-2}\right]={\left[{\mathrm{LT}}^{-1}\right]}^{\mathrm{x}}{\left[{\mathrm{MLT}}^{-2}\right]}^{\mathrm{y}}{\left[{\mathrm{LT}}^{-2}\right]}^{\mathrm{z}}$

$\left[\mathrm{M}\right]\left[{\mathrm{L}}^{-1}\right]\left[{\mathrm{T}}^{-2}\right]={\left[\mathrm{M}\right]}^{\mathrm{y}}\left[{\mathrm{L}}^{\mathrm{x}+\mathrm{y}+\mathrm{z}}\right]\left[{\mathrm{T}}^{-\mathrm{x}-2\mathrm{y}-2\mathrm{z}}\right]$

$\Rightarrow y=1, x+y+z=-1; -x-2y-2z=-2$

$x+z=-2 x+2y+2z=2$

$z=2, x=-4 x+2z=0$

$\left|\mathrm{Y}\right|=\left[{\mathrm{V}}^{-4}{\mathrm{A}}^2\mathrm{F}\right]$