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 ?

Let F be the upthrust of the air. As the balloon is descending down with an acceleration a.∴ mg−F=ma  ....(i)Let mass m0 be removed from the balloon so that it starts moving up with an acceleration a. Then,F−m−m0g=m−m0aF−mg+m0g=ma−m0a                           . . . .(ii) Adding eqn. (i) and eqn. (ii), we get m0g=2ma−m0am0g+m0a=2mam0(g+a)=2mam0=2mag+a