Question 7: Show that (a) KE = ½ mv2 (b) PEg = mgh
If the dimensions on both sides of the equations are same, the equations will be equal. Since the dimensions of energy are,
J = N m ⇒ J = kg ms-2, therefore, dimensions of energy = [M][LT-2] = [MLT-2] …. (A)
In order the given equations to be correct, each equation must have these dimensions.
Dimensions of KE
Comparing with the dimensions of energy in (A), we see both dimensions are same. Therefore, KE=1/2mv2
Dimensions of PE
Again compare with equation (A), we see the dimensions are same. Therefore, PEg = mgh.