A balloon with mass ‘m’ is descending down with an acceleration ‘a’ (where a < g). How much mass should be removed from it so that it starts moving up with an acceleration ‘a’?

\(\frac{2 ma}{g+a}\)

Let up thrust of air be F_b then for downward motion mg – F_b = ma

Let's assume that mass m' be removed from the balloon

So when it start moving upward

F_b - (m - m') g = (m - m')a

m' = \(\frac{2ma}{g+a}\)