Question

A balloon of mass $M$ is descending with a constant acceleration $g/3$. When a mass $m$ is released from the balloon it starts rising with the same acceleration $g/3$. The value of $m$ is (Assuming that its volume does bot change):

Answer 1

While descending

$R=M(g-a)$

$R=M(g-\frac{g}{3})$

$R=\frac{2}{3}Mg$

While rising

$R=(M-m)(g+a)$

$\frac{2}{3}Mg=(M-m)(g+\frac{g}{3})$

$\frac{2}{3}Mg=(M-m)\frac{4}{3}g$

$M=(M-m)2$

$\frac{M}{2}=M-m$

$m=M-\frac{M}{2}$

$m=\frac{M}{2}$

Mass to be released $=\frac{M}{2}$