Gravitational potential energy is linearly proportional to height

Steps:

• Gravitational potential energy is given by E_p = mgh, where m is mass and g is gravitational acceleration.
• Mass m and g are constants for the object near Earth's surface.
• Thus, E_p varies directly with height h, with no other dependencies.
• The graph of E_p versus h is a straight line passing through the origin.

Why A is correct:

• Option A depicts a straight line with positive slope from the origin, directly matching the linear relationship E_p = mgh.

Why the others are wrong:

• B shows a curve, but the relationship is linear, not quadratic or exponential.
• C is horizontal, implying constant E_p regardless of h, which violates E_p = mgh.
• D decreases with h, but E_p increases as height rises.

Final answer: A