Question

A balloon of mass M is descending at a constant acceleration $\alpha$ When a mass m is released from the balloon it starts rising with the same acceleration a, assuming that its volume does not change, 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)

Suppose F = upthrust due to buoyancy
Then while descending, we find
$Mg-F=M \alpha\ldots (i)$
when ascending, we have
$F-(M-m)g=(M-m) \alpha \ldots(ii)$
Solving equations (i) and (ii), we get:
$m=\left[\frac{2\alpha}{\alpha+g}\right]M$