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Concepts Of Physics MCQ Edition [Volume 1]PhysicsNewton's Laws of Motion

A constant upward buoyancy force B is exerted by the atmosphere on a balloon. The air resistance acting on the balloon is proportional to its velocity and opposes its motion. Carrying a mass M , the balloon is observed to fall near the earth's surface at a constant velocity v . Determine the amount of mass that must be removed from the balloon for it to rise at a constant velocity v .

Options

  1. A2M - B g
  2. B2B g - M
  3. CM - B g
  4. D2 (M - B g )

Correct answer

D. 2 (M - B g )

Step-by-step solution

Let the air resistance be kv . When the balloon falls with a constant velocity v , the air resistance acts upwards. Equating the forces for zero net force: Mg = B + kv kv = Mg - B Let M' be the new mass of the balloon when it rises with the same constant speed v . The air resistance now acts downwards. Equating the forces: B = M'g + kv Substituting the value of kv from the first equation: B = M'g + (Mg - B) M'g = 2B - Mg M' = 2B g - M The amount of mass that must be removed is: M = M - M' M = M - ( 2B g - M ) M = 2

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