question_answer

A balloon with mass M is descending down with an acceleration a(< g). What mass m of its contents must be removed so that it starts moving up with an acceleration a?

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) \[m=\frac{2Ma}{g+a}\]