a ballon of mass M is desending at a constantacceleration g/3. when mass m is released from the balloon it starts rising with the same acceleration g/3. assuming that its volume does not change, what is the value of m.

Let the force due to buoyancy be B.In the first case the equation will beMg - B = Mg/3In the second case the equation will beB - (M-m)g = (M-m)g/3Since the volume is unchanged, the force of Buoyancy remains unchanged as same amount of air is displaced even now and the new mass is (M-m)Adding the two equations we get,mg = (2M-m)g/3or m(g+g/3)=2Mg/3or m=2Mg/(g+g/3)3or m= 18Mg/4gor m= 9M/2