Ratio of potential energy gain to work by applied force on incline

Steps:

• Height gained h = s sin α, so gravitational PE gain = m g h = m g s sin α.
• At constant velocity, force F acts parallel to slope, so work by F = F s.
• Ratio = (m g s sin α) / (F s) = m g sin α / F.
• This follows from work-energy theorem, as net work equals PE change.

Why D is correct:

• D equals the derived ratio using PE formula mgh and work W = F s under constant velocity (net force zero, F balances mg sin α component).

Why the others are wrong:

• A: Identical to D, but listed as distractor; correct form is D.
• B: Involves velocity v, irrelevant to energy ratio without kinetic change.
• C: Simplifies to F/(2s), resembling kinetic energy formula but ignores gravity and constant speed.

Final answer: D