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A balloon of mass M is attached via a light rope of length L to a man of mass m standing below it. The entire system is stationary and in equilibrium in air (buoyant force equals total weight). The man then climbs up the rope until he reaches the top. Which of the following statements is/are correct? (A) The balloon descends a distance of L. (B) The man ascends a distance of mL/(m+M) relative to the ground. (C) The gravitational potential energy of the man increases. (D) The net change in gravitational potential energy of the system (man + balloon) depends on the mass ratio m/M.

1. The balloon descends a distance of L.
2. The man ascends a distance of mL/(m+M) relative to the ground.
3. The gravitational potential energy of the man increases.
4. The net change in gravitational potential energy of the system (man + balloon) depends on the mass ratio m/M.

Correct answer: The gravitational potential energy of the man increases.

Solution

Since the CM is fixed, man rises by ML/(M+m) and balloon descends by mL/(M+m). Man's height increases so his PE increases (option C), while balloon falls the same energy worth, leaving net GPE unchanged and independent of mass ratio.

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