A rope ladder with length l 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 air. As the man climbs up the ladder into the balloon, the balloon descends by a height h. Then the potential energy of the balloon a. decreases by mgh b. increases by mgh c. increases by mgl d.increases by mg(l-h)

Asked by Pallavi Chaturvedi | 18th Oct, 2013, 05:22: PM

Expert Answer:

The man climbs up the ladder. Hence, work done by man is mgl.
This work done goes as increase in potential energy. The man climbs up the ladder and the balloon descends by height h.
 
Thus, gain in potential energy by man is mgl - mgh
 
If ?E is the change in potential energy of the balloon, then work done by man goes as gain in potential energy of himself and change in potential energy of balloon.
 
mgl = mgl - mgh + ?E
 
Thus, ?E = mgh
 
That is, the potential energy of balloon increases by mgh.
Thus, option b is correct.

Answered by Romal Bhansali | 21st Oct, 2013, 12:50: PM

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