The force of buoyancy exerted by the atmosphere on a balloon is B in the upward direction and remains constant. The force of air resistance on the balloon acts opposite to the direction of velocity and is proportional to it. The balloon carries a mass M and is found to fall down near the earth’s surface with a constant velocity u. How much mass should be removed from the balloon so that it may rise with a constant velocity u?
Given:
Buoyancy force = B
Velocity in both cases =
Air resistance is proportional to velocity 
∴ resistive force = 
, where k is proportionality constant.
Case I:
When balloon is falling down with constant velocity,
Then equation for equilibrium becomes,
Case II:
When balloon is raising up with constant velocity after removing some mass,
Then equation for equilibrium becomes,
∴ 
∴ removed mass = 