A balloons of mass M is descending at a constant acceleration `alpha`. When a mass m is released from the balloon, it starts rising. With the same acceleration `alpha`. Assuming that its volumes does not change, what is the valule of m?

Options

A. `(alpha)/(alpha + g) M`
B. `(2alpha)/(alpha + g) M`
C. `(alpha + g)/(alpha)M`
D. `(alpha + g)/(2 alpha)M`

Answer

B

Explanation

Suppose F=upthrust due to buoyancy
Then while decending, we find
`Mg-F=Ma` …(i)
When ascending, we have
`F=(M-m)g=(M-m)a`…(ii)
Solving Eqs. (i) and (ii), we get `m=[(2 alpha)/(alpha-g)]M`.