Question

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

Answer 1

Answer: (B)

$\frac{2Ma}{(g+a)}$

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 $F=Mg-Ma....\left(i\right)$
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)
$Ma-ma=Mg-Ma-Mg+mg$
$\Rightarrow m=\frac{2Ma}{(g+a)}$.