A balloon with mass ‘ $\mathrm{m}$ ‘ is descending down with an acceleration ‘a’ (where $\mathrm{a}Option A $\quad \frac{2 m a}{g+a}$
Option B $\quad \frac{2 \mathrm{ma}}{\mathrm{g}-\mathrm{a}}$
Option C $\quad \frac{\mathrm{ma}}{\mathrm{g}+\mathrm{a}}$
Option D $\quad \frac{\mathrm{ma}}{\mathrm{g}-\mathrm{a}}$

The correct option is A

Let $\mathrm{F}_{\mathrm{b}}$ be the up thrust of air and then for downward motion,

$\mathrm{mg}-\mathrm{F}_{\mathrm{b}}=\mathrm{ma}$

Let $\mathrm{m}$’ be the mass removed from the balloon

So when it start moving upward, we have,

$\mathrm{F}_{\mathrm{b}}-\left(\mathrm{m}-\mathrm{m}^{\prime}\right)=\left(\mathrm{m}-\mathrm{m}^{\prime}\right) \mathrm{a}$

$\mathrm{m}^{\prime}=\frac{2 \mathrm{ma}}{\mathrm{g}+\mathrm{a}}$