question_answer

A balloon with mass M is descending down with an acceleration a (a < g). What mass' of its contents must be removed so that it starts moving up with same acceleration a

A)  \[\frac{2M\left( g \right)}{a}\]

B) \[\frac{M\left( g+a \right)}{g}\]

C)  \[\frac{Mg}{g+a}\]

D) \[\frac{2Ma}{g+a}\]

Correct Answer: D

Solution :

[d]

Up thrust F will remain same in both the cases.
Equations of motion be:
\[MgF=Ma\]	...(1)
and    \[F-(M-m)g=(M-m)a\]	...(2)
solving equations (1) and (2) we get, mass to be removed \[m=\frac{2Ma}{g+a}\]