A balloon has mass of 10 g in air. The air escapes from the balloon at a uniform rate with velocity 4.5 cm / s. If the balloon shrinks in 5 s completely. Then, the average force acting on that balloon will be (in dyne).

Solution

Physics sir · 4 steps

Treat the balloon like a rocket: thrust is the exhaust speed times the rate at which mass leaves.

1. Thrust formula. Air leaving the balloon carries momentum away, so the balloon gets an equal push the other way. For a uniform escape rate, the force is the relative speed of the escaping air times the mass lost per second.

   F = vᵣₑₗ dm/dt

2. Mass rate. All 10 g of air leaves in 5 s at a uniform rate. So dm/dt = 10/5 = 2 g s⁻¹.
3. Put in numbers. F = 4.5 cm s⁻¹ × 2 g s⁻¹ = 9 g cm s⁻². One g cm s⁻² is one dyne, so there is no unit conversion to do.
4. So. The average force on the balloon is 9 dyne, option (b).

The idea to keep. Whenever mass leaves a body at a steady rate, the push on the body is vᵣₑₗ × dm/dt. Stay in CGS units and the answer comes out directly in dyne.

Answer from the NTA final answer key. Solution by PrepWiser.