Deriving potential energy from work against gravity

Steps:

• Gravitational potential energy gain equals work done to lift the object against gravity.
• Force required is weight, mg, acting downward.
• Displacement is vertical height h upward, opposite to force.
• Work done W = force × distance = mgh, so ΔE_p = mgh.

Why D is correct:

• The definition of work done (W = F × d × cosθ) directly yields ΔE_p = mgh when F = mg and θ = 180° for lifting.

Why the others are wrong:

• A. Not specified, so irrelevant.
• B. Momentum (p = mv) relates to motion, not energy storage from height.
• C. Power (P = W/t) involves time, absent in the static ΔE_p equation.

Final answer: D