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  4. A rope ladder of length L is attached to a balloon of mass M. As the man of mass m climbs the ladder into the balloon basket, the balloon comes down by a vertical distance s. Then the increase in potential energy of man divided by the increase in potential energy of balloon is

Q. A rope ladder of length $L$ is attached to a balloon of mass $M$. As the man of mass $m$ climbs the ladder into the balloon basket, the balloon comes down by a vertical distance $s$. Then the increase in potential energy of man divided by the increase in potential energy of balloon isPhysics Question Image

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Solution:

Work done by man, $m g L=m g(L-s)+m g s$
where $m g(L-s)$ is the increase in potential energy of the man and $m g s$ is the increase in potential energy of the balloon because the balloon would have been lifted up but for the climbing of the man. So
$\frac{\text { Increase in PE of man }}{\text { Increase in PE of baloon }}=\frac{m g(L-s)}{m g s}-\frac{L-s}{s}$

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