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?

Options

A. `(2ma)/(g + a)`
B. `(2ma)/(g -a)`
C. `(ma)/(g +a)`
D. `(ma)/(g -a)`

Answer

a

Explanation

Let `F` be the upthrust on balloon due to air
Case (i) When balloon is descending down with
acceleration a then as shown in
`mg - F = ma`
Case (ii) Let `m_(0)` be the mass removed from the ballon then balloon moves upwards with acceleration
Now `F - (m - m_(0)) g = (m - m_(0))` a ..(ii)
Adding (i) and (ii) we get
`mg - (m - m_(0)) g = ma + (m -m_(0))a`
Solving it we get `m_(0) = (2ma)/(g + a)`
.