Work by gravity over a closed path is zero

Steps:

• The ball travels from point P upward to maximum height h and back down to Q at the same level as P.
• Gravitational force is conservative, so work depends only on initial and final positions.
• Net displacement in height from P to Q is zero.
• Thus, total work by gravity is zero.

Why A is correct:

• For a conservative force like gravity, work over any closed path (net displacement zero) is zero by definition.

Why the others are wrong:

• B: (1/2)mv² is kinetic energy at P, not work by gravity.
• C: mgh is work by gravity for ascent only, ignoring descent.
• D: 2mgh double-counts potential energy change, but net change is zero.

Final answer: A