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?

Answer

`(2Ma)/(g +a)` .

Explanation

Let`F` be the upthrust of air in either case
In(i) case, `Mg - F = Ma` …(i)
In (ii) case `F - (M -m) g = (M - m) a` …(ii)
using (i) `(Mg - Mg) - Mg + mg = Ma - ma`
or `m (g +a) = 2 Ma`
`m = (2Ma)/(g + a)` .