Given equation $\frac{1}{2}m{v}^2=mgh,$  where m is the mass of the body, v is velocity, g is the acceleration due to gravity and h is the height. Then the given equation is

Given, $\frac{1}{2}m{v}^2=mgh$

The dimensions of LHS are

$\left[M\right]{\left[L{T}^{-1}\right]}^2=\left[M\right]=\left[L^2{T}^{-2}\right]=\left[M{L}^2{T}^{-2}\right]$

The dimensions of RHS are

$\left[M\right]\left[L{T}^{-2}\right]\left[L\right]=\left[M\right]\left[L^2{T}^{-2}\right]=\left[M{L}^2{T}^{-2}\right]$

The dimensions of LHS and RHS are the same and hence the equation is dimensionally correct.