Question Detail
Question
If force, time, and velocity are treated as fundamental quantities, then the dimensional formula of energy is:
Correct Answer
Option D is the correct answer.
Detailed Explanation
Energy = work = force × distance. Distance = velocity × time. So energy = force × (velocity × time) = F V T. So dimensions [F][V][T]. That's F T V. But that's option A. However, energy also = ½ mv². If F, T, V are fundamental, then mass = F / acceleration = F / (V/T) = FT/V. So energy = (FT/V) * V² = F T V. So [FTV]. But option D is FT²V². Possibly they want [FTV]. Given answer D, we'll note discrepancy.
Hint
Express energy in terms of force, time, velocity.