Gravitational force as negative gradient of potential energy

Steps:

• Gravitational potential energy ΔU = mgh, linear with vertical distance h in uniform field.
• Force F = -d(ΔU)/dh, derivative of linear function yields constant magnitude.
• Thus, F remains constant regardless of distance x moved.
• Graph of F vs. x is horizontal line, matching option C.

Why C is correct:

• By definition, F = -∇U; uniform field implies constant F, so straight horizontal line.

Why the others are wrong:

• A: Shows increasing F, implying accelerating field, not uniform.
• B: Shows decreasing F, suggesting inverse variation, unlike constant gravity.
• D: Oscillatory F, unrelated to steady gravitational field.

Final answer: C