A balloon with mass m is descending down with an acceleration a (where, a < g ). How much mass should be removed from it so that it starts moving up with an acceleration a ?

Step-by-step solution

When the balloon is descending down with an acceleration a , where, B= buoyant force. Here, we should assume that while removing some mass the volume of balloon and hence buoyant force will not change. Let the new mass of the balloon is m^ , so On solving Eqs. (i) and (ii), we get aligned & m g-m^ g=m a+m^ a & m(g-a)=m^ (g+a) m^ = m(g-a) g+a aligned So, mass removed, m=m-m^ =m [1- (g-a) (g+a) ]=m [ g+a-g+a g+a ]= 2 m a g+a