question_answer

If a balloon of mass M is descending down with an acceleration \[a(<g),\]then what is the value of mass \[m\] (of its contents) that must be removed so that it starts moving up with an acceleration a?

A) \[\frac{Ma}{(g+a)}\]

B)  \[\frac{2Ma}{(g+a)}\]

C)  \[\frac{M}{(g+a)}\]

D)  Not possible

Correct Answer: B

Solution :

Let the retarding force acting on the balloon in vertically upward direction be F. When      the      balloon      is  descending  down with acceleration a, its equation of motion can be given as        \[~Ma=Mg-F\] or        \[F=Mg-Ma\] ?(i) Let M mass is removed from the balloon. When it moves up with acceleration a, its equation of motion can be given as \[(M-m)a=F-(M-m)g\] From Eq. (i) \[Ma-ma=Mg-Ma-Mg+mg\] \[\Rightarrow \] \[m=\frac{2Ma}{(g+a)}\]