Dimensional Analysis of Units Steps:

• Determine dimensional formula for distance: [L].
• Determine dimensional formula for force: [M L T^{-2}].
• Determine dimensional formula for power × time: power is [M L^{2} T^{-3}], multiplied by time [T] gives [M L^{2} T^{-2}].
• Compare exponents of length (L): A, B, and D have L^{1}; C has L^{2}.

Why C is correct:

• Power × time equals energy (from work-energy theorem, W = P t), with dimensional formula [M L^{2} T^{-2}], featuring L^{2} unlike the L^{1} in the others.

Why the others are wrong:

• A: Distance has [L], with L^{1}.
• B: Force has [M L T^{-2}], with L^{1}.
• D: Rate of change of momentum equals force (Newton's second law, F = dp/dt), with [M L T^{-2}] and L^{1}.

Final answer: C