If force [ F ] , acceleration [ A ] and time [ T ] are chosen as the fundamental physical quantities. Find the dimensions of energy.

Step-by-step solution

Let consider, [ Energy ] = [ F ] a [ A ] b [ T ] c Now put the dimensional formula of the given quantities, ML 2 T - 2 = MLT - 2 a LT - 2 b [ T ] c ML 2 T - 2 = M a L a + b T - 2 a - 2 b + c On comparing powers of [ M ] a = 1 On comparing powers of [ L ] a + b = 2 ⇒ 1 + b = 2 ⇒ b = 1 On comparing powers of [ T ] - 2   a - 2   b + c = - 2 ⇒ - 2 - 2 + c = - 2 ⇒ c = 2 [   E n e r g y   ] = [ F ] [ A ] T 2