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Question

# A rope ladder with a length l metres carrying a man with a mass m at its end is attached to the basket of a balloon with a mass M. The entire system is in equilibrium in the air. As the man climbs up the ladder into the balloon, the balloon descends by a height h. In this case, the potential energy of the balloon:

A
decreases by mgh
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B
increases by mgh
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C
increases by mg(lh)
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D
increases by mgl
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Solution

## The correct option is A increases by mghThe formula for potential energy due to gravity is PE=mgh. The total work done by the man is given as mgl where l is the length of the ladder.As the man moves up the rope, the balloon descends a height h.So, gain in potential energy of the man is mgl−mgh.If dE be the change in potential energy of the balloon, then by conservation of energy, Total Work done = Change in Potential energy of the system.So, we have,mgl = mgl − mgh + dE. That is, dE =mgh.Hence, the potential energy of the balloon increases by mgh.

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