Question

The balloon, the light rope and the monkey shown in figure are at rest in the air. If the monkey reaches the top of the rope, by what distance does the balloon descend?
Mass of the balloon $=M$, mass of the moneky $=m$ and the length of the rope ascended by the monkey $=L$.

Answer 1

Monkey and Balloon are at rest initially

Centre of mass is at '$P$'

Monkey descends through a distance '$L$'

shifted center of mass

$\left(t_0\right)=\frac{(m\times L+M\times 0)}{M+m}$

$=\frac{mL}{(M+m)}$

therefore the ballon descends through a distance $\frac{mL}{M+m}$ from $p$