Question

What is the value of m?

A balloon is descending at a constant
acceleration a . The mass of the baloon is
M. When a mass m is released from the
balloon, it starts rising with the same
acceleration a . Assuming that the volume
does not change when the mass is released,
what is the value of m?

Answer 1

`m = (2Ma)/(g+a)`

Explanation:

Let the buoyant force acting on the balloon be `B`.

Newton's second law gives us

`Mg-B=Ma`

again, after the mass `m` is released, (since the volume of the balloon does not change in the process, the buoyant force stays the same), we have

`(M-m)g-B = -(M-m)a`

We can eliminate the unknown `B` by subtracting these two equations

`mg = (2M-m)a implies m(g+a) = 2Ma implies`

`m = (2Ma)/(g+a)`