Let us consider an equaiton
`(1)/(2)mv^2 = mgh,`
Where m is the mass of the body, `upsilon` its velocity, g is acceleration due to gravity and h is the height. Cheak whether this equation is dimensionally correct.

Explanation

The dimensions of LHS are
`[M] [LT^(-1)]^(2)=[M] [L^(2)T^(-2)]`
`= [M L^(2) T^(-2)]`
the dimensions of RHS are
`[M] [LT^(-2)] [L]=[M] [L^(2)T^(-2)]`
`=[M L^(2) T^(-2)]`
The dimensions of LHS and RHS are the same and hence the equation is dimensionally correct.