Work by tension equals gain in potential energy

Steps:

• Weight rises height q, increasing gravitational potential energy by Wq.
• Starts and ends at rest, so kinetic energy change is zero.
• Work-energy theorem: net work on weight equals zero.
• Work by gravity is -Wq; thus, work by tension is +Wq.

Why C is correct:

• Matches work-energy theorem: tension does work Wq to offset gravity's -Wq, yielding net zero work for zero kinetic energy change.

Why the others are wrong:

• A: Wp uses undefined or irrelevant p, ignoring vertical rise q.
• B: W(p + q) incorrectly adds horizontal distance to vertical work.
• D: Wr considers only horizontal displacement r, where vertical tension does no work.

Final answer: C