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(B) Let $F$ be the upward buoyant force acting on the balloon.In the first case,the balloon of mass $M$ descends with acceleration $a$. According to N

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$\frac{2 M a}{(a+g)}$

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(B) Let $F$ be the upward buoyant force acting on the balloon.In the first case,the balloon of mass $M$ descends with acceleration $a$. According to Newton's second law:$M g - F = M a \Rightarrow F = M g - M a$ ...$(i)$In the second case,a mass $M^{\prime}$ is removed,so the new mass is $(M - M^{\prime})$. The balloon now ascends with acceleration $a$. According to Newton's second law:$F - (M - M^{\prime}) g = (M - M^{\prime}) a$Substituting $F$ from Eq. $(i)$:$(M g - M a) - (M - M^{\prime}) g = (M - M^{\prime}) a$$M g - M a - M g + M^{\prime} g = M a - M^{\prime} a$$M^{\prime} g + M^{\prime} a = M a + M a$$M^{\prime} (g + a) = 2 M a$$M^{\prime} = \frac{2 M a}{g + a}$

$A$ balloon of mass $M$ descends with an acceleration $a (< g)$. What mass needs to be removed from the balloon so that it starts ascending with acceleration $a$?

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