Question

A balloon of mass M is descending with a constant acceleration $g/3$ when a mass m is released from the balloon it starts rising with the same acceleration $g/3$. The value of m is (Assuming that its volume does not change):-

• A. $\frac{M}{2}$
• B. $\frac{M}{4}$
• C. $4M$
• D. $2M$

Answer 1

The correct option is

C

$\frac{M}{2}$

Diagram for the given situation

While descending the force acting on the balloon,

$R=M(g-a)R=M(g-\frac{g}{3})R=\frac{2Mg}{3}$

While rising,

$R=(M-m)(g+a)\frac{2Mg}{3}=(M-m)(g+\frac{g}{3})=(M-m)\frac{4g}{3}M=(M-m)2\frac{M}{2}=M-mm=\frac{M}{2}$

$\therefore$ Mass to be removed $=\frac{M}{2}$