• # 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

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