Question

A man of mass $m$ , a light rope and a balloon of mass $M$ are at rest in air as shown. Then, the man starts climbing the rope and reaches the top. Assume the crate in which the man is standing to be light,

• A. The balloon descends by a distance $\frac{m L}{M + m}$ .
• B. The balloon ascends by a distance $\frac{m L}{M + m}$ .
• C. The balloon descends by a distance $\frac{M L}{M + m}$ .
• D. The balloon ascends by a distance $\frac{M L}{M + m}$ .

Answer 1

Answer: (A)

Let $x$ be the distance of centre of mass from the balloon.
$m\left(L - x\right)=Mx\Rightarrow x=\frac{m L}{m + M}$