A balloon of mass M is descending vertically with acceleration a. How much weight must be thrown from the case attached to the balloon so that it begins to ascend vertically with acceleration a? Assume that upward lift of air in the balloon does not change?

Take upward direction to be the positive y-direction. If m is the mass thrown out, then the equation of motion for before and after the mass m is thrown out are

Ma = F – Mg

(M–m)a = F – (M–m)g

Solving the two equations m =2ma/(a+g)

Regards

Arun (askIITians forum expert)