一氫氣球 以一輕繩懸吊另一質量為M的物體

Let F be the buoyance force
Mg - F = Ma
where g is the acceleration due to gravity

When the balloon is moving upward with acceleration a,
F - M'g = M'a
where M' is the new mass suspended on the balloon

Adding the two equations:
Mg - M'g = Ma + M'a
M'(a + g) = M(g - a)
M' = M(g-a)/(g+a)

Hence, mass that needs to be thrown away
= M - M'
= M - M(g-a)/(g+a)
= 2agM/(g+a)