Question

A balloon with mass `m` is descending down with an acceleration a `(where altg)` . How much mass should be removed from it so that it starts moving up with an acceleration a?
A. `(2ma)/(g+a)`
B. `(2ma)/(g-a)`
C. `(ma)/(g+a)`
D. `(ma)/(g-a)`

Answer 1

Correct Answer - A
Force acting on balloon are its weight and buoyant force `(B)` . The buoyant force will be constant as there is no change in volume of the balloon.
When balloon is descending down
`mg-B=ma` (i)
When balloon is moving up
`B-(m-m_(0))g=(m-m_(0))a` (ii)
Equation (i) +equation (ii)
implies `mg-mg+m_(0)g=ma+ma-m_(0)a`
implies `m_(0)=(2ma)/(g+a)` .