Efficiency equals useful work output divided by work input

Steps:

• Identify useful work output: force of gravity times vertical height, W × h.
• Identify work input: applied force P times distance along slope, P × d.
• Compute efficiency: ratio of output to input, (W h) / (P d).
• Select matching expression from choices.

Why D is correct:

• Matches definition of mechanical efficiency as useful work (against gravity, Wh) over total work done (by P, Pd).

Why the others are wrong:

• A: Uses undefined F and inverts ratio, yielding input/output instead of efficiency.
• B: Inverts correct ratio, giving work input over output (not efficiency).
• C: Uses undefined F instead of P, with correct ratio but wrong input work.

Final answer: D