Gravitational PE gain is mgh; for constant ΔPE, h ∝ 1/m

Steps:

• Gravitational potential energy gain ΔPE = mgh, where g is constant.
• If ΔPE is the same for all objects, then mgh = constant.
• Rearrange to h = constant / (mg), so h decreases as m increases.
• Graph of h vs. m is a decreasing hyperbola.

Why A is correct:

• Option A shows h inversely proportional to m, matching ΔPE = mgh for constant ΔPE.

Why the others are wrong:

• B shows direct proportion (h increases with m), violating inverse relation in ΔPE = mgh.
• C shows constant h (independent of m), ignoring mass effect on PE.
• D shows h increasing then decreasing or unrelated trend, not matching hyperbolic inverse.

Final answer: A