Question

The balloon, the light rope and the monkey shown in fig. 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$=M$, the mass of the monkey $=m$ and the length of the rope ascended by the monkey$=L$

Answer 1

The centre of mass is given by :

$x_{cm}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}$

where m₁ is the mass of monkey and m₂ is the mass of balloon.

Here, balloon and monkey initially at rest. When monkey descends through a distance L, the centre of mass gets shifted.

Now shifted centre of mass is

$x^{{}^{\prime }}=\frac{m_1\times L+0}{m_1+m_2}$

$=\frac{m_{1}L}{m_1+m_2}$

Hence, balloon descends through a distance $\frac{m_{1}L}{m_1+m_2}$ from the centre of mass.