Question

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

• A. $\frac{L-s}{s}$
• B. $\frac{L}{s}$
• C. $\frac{s}{L-s}$
• D. $L-s$

Answer 1

Answer: (A)

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
$\frac{\text { Increase in PE of man }}{\text { Increase in PE of baloon }}=\frac{m g(L-s)}{m g s}-\frac{L-s}{s}$