Check whether the equation F.S = 1/2(mv^2 - mu^2) is dimensionally correct, where m is mass of the body, v its final velocity,u its initial velocity, F is force applied and S is the distance moved.
We know the dimension of force as [MLT-2]
and the dimension of v and u = [LT-1]
and the dimension of s=[L] and dimension of mass=[M]
∴[MLT-2] x [L] = [M][LT-1]2 + [M][LT-1]2
[ML2T-2] = [ML2T-2] + [ML2T-2]
∴ THIS EQUATION IS DIMENSIONALLY CORRECT
and the dimension of v and u = [LT-1]
and the dimension of s=[L] and dimension of mass=[M]
∴[MLT-2] x [L] = [M][LT-1]2 + [M][LT-1]2
[ML2T-2] = [ML2T-2] + [ML2T-2]
∴ THIS EQUATION IS DIMENSIONALLY CORRECT