# 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 =

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