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(B) Let $F$ be the upthrust (buoyant force) acting on the balloon.When the balloon is descending with acceleration $\alpha$,the net force equation is:

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$\left[ \frac{2\alpha}{\alpha + g} \right] M$

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(B) Let $F$ be the upthrust (buoyant force) acting on the balloon.When the balloon is descending with acceleration $\alpha$,the net force equation is:$Mg - F = M\alpha$  --- $(i)$When a mass $m$ is released,the new mass of the balloon becomes $(M - m)$. It starts rising with the same acceleration $\alpha$. The net force equation is:$F - (M - m)g = (M - m)\alpha$  --- $(ii)$From equation $(i)$,we have $F = Mg - M\alpha = M(g - \alpha)$.Substitute this value of $F$ into equation $(ii)$:$M(g - \alpha) - (M - m)g = (M - m)\alpha$$Mg - M\alpha - Mg + mg = M\alpha - m\alpha$$mg + m\alpha = 2M\alpha$$m(g + \alpha) = 2M\alpha$$m = \left[ \frac{2\alpha}{\alpha + g} \right] M$

$A$ 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 $\alpha$. Assuming that its volume does not change,what is the value of $m$?

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