Question

A balloon is descending at a constant acceleration $\alpha$. The mass of the balloon is $M$. When a mass $m$ is released from the balloon, it starts rising with the same acceleration $\alpha$. Assuming that the volume does not change when the mass is released, what is the value of $m$ ?

• A. $\frac{\alpha }{\alpha +g}M$
• B. $\frac{2\alpha }{\alpha +g}M$
• C. $\frac{\alpha +g}{\alpha }M$
• D. $\frac{\alpha +g}{2\alpha }M$

Answer 1

Answer: (B)

$\frac{2\alpha }{\alpha +g}M$

Let the buoyant force acting on balloon due to air = $F$, upwards.

Thus before the mass is released,

$M\alpha =Mg-F$......(i)

After the mass is released,

$(M-m)\alpha =F-(M-m)g$......(ii)

Solving both equations to eliminate $F$ gives,

$m=\frac{2\alpha }{\alpha +g}M$