Answer:
Let
the retarding force acting on the balloon in vertically upward direction be F.
When the
balloon is descending down with acceleration a. Fig.3(HT). 1, its equation of
motion can be written as
Ma = Mg ? F or F = Mg ? Ma
Let a mass m be removed from the
balloon. As it moves up with an acceleration a, as shown in Fig. 3(HT).1, its
equation of motion can be written as
\[\left( M-m \right)a=F-\left(
M-m \right)g\]
using(i), Ma ? ma = Mg ? Ma ? Mg
+ mg
2Ma = m (g + a)
\[m=\frac{2Ma}{g+a}\]
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