Q. 194.6( 9 Votes )

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?

Answer :


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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