To solve this problem, we need to analyze the forces acting on the balloon in both scenarios: when it is descending and when it is ascending.$\\$1. When the balloon is descending with acceleration $a: \\$• The gravitational force acting on the balloon is $mg. \\$• The net force acting on the balloon is $F_{net} = m(g - a). \\$• This net force is due to the buoyant force $B$ acting upwards.$\\$Therefore, $B = m(g - a). \\$2. When the balloon starts moving up with acceleration $a: \\$• Let $m'$ be the new mass of the balloon after removing some mass.$\\$• The net force required for upward acceleration is $F'_{net} = m'(g + a). \\$• The buoyant force remains the same, $B = m(g - a). \\$Therefore, $m'(g + a) = m(g - a). \\$3. Solving for $m': \\ m'(g + a) = m(g - a) \\ m' = \frac{m(g - a)}{g + a} \\$4. Finding the mass to be removed:$\\$• The mass removed is $m - m'. \\ m - m' = m - \frac{m(g - a)}{g + a} \\ = m \left(1 - \frac{g - a}{g + a}\right) \\ = m \left(\frac{(g + a) - (g - a)}{g + a}\right) \\ = m \left(\frac{2a}{g + a}\right) \\$Therefore, the mass that should be removed is $\frac{2ma}{g + a}. \\$This corresponds to Option 1.