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)                 \[Ma-ma=Mg-Ma-Mg+mg\] \[\Rightarrow \]               \[m=\frac{2Ma}{(g+a)}\]