Consider the equation $\frac{1}{2} m v^{2} = m g h$,where $m$ is the mass of the body,$v$ is the velocity,$g$ is the acceleration due to gravity,and $h$ is the height. Is this equation dimensionally correct?

(N/A) The dimensions of the $LHS$ are:
$[M][LT^{-1}]^{2} = [M][L^{2}T^{-2}] = [ML^{2}T^{-2}]$
The dimensions of the $RHS$ are:
$[M][LT^{-2}][L] = [M][L^{2}T^{-2}] = [ML^{2}T^{-2}]$
Since the dimensions of the $LHS$ and $RHS$ are the same,the equation is dimensionally correct.