A balloon 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 volume does not change, what is the value of m?

Options

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

Answer

B

Explanation

Suppose `F` =upthrust due to buoyancy
Then while descending, we find
`Mg-F=Malpha`
when ascending, we have `F-(M-m)g=(M-m)alpha`
Solving equation (i) and (ii), we get: `m=[(2alpha)/(alpha+g)]M`