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 monkey = m and the length of the rope ascended by the monkey = L. 

Answer 1

Given:
The mass of monkey is m.
The mass of balloon is M. 

Initially, the monkey, balloon and the rope are at rest.

Let the centre of mass is at a point P.

When the monkey descends through a distance L,

The centre of mass shifts.

\[l_0 = \frac{m \times L + M \times 0}{M + m}\]

\[ = \frac{mL}{M + m} \text{ from P }\]
Therefore, the balloon descends through a distance
\[\frac{mL}{M + m}\].