A machine gun of mass 10 kg fires 20 g bullets at the rate of 180 bullets per minute with a speed of 100 m s⁻¹ each. The recoil velocity of the gun is

Solution

Physics sir · 3 steps

Count the momentum the bullets carry away in one second; the gun takes the same amount backwards.

1. Bullets per second. 180 bullets per minute is 180/60 = 3 bullets every second. Each bullet has mass 20 g = 0.02 kg.
2. Momentum balance. Gun and bullets start at rest, so their total momentum stays zero. The forward momentum the bullets carry away each second must equal the backward momentum the gun picks up in that second.

   M v = n m u ⇒ v = (3 × 0.02 × 100)/10 = 6/10 = 0.6 m s⁻¹

3. So. The bullets carry away 6 kg m s⁻¹ every second, so the 10 kg gun gains a recoil velocity of 0.6 m s⁻¹ in each second of firing. That is option (d).

The idea to keep. For a gun firing a steady stream of bullets, work per second: bullets per second times the momentum of one bullet gives the gun's recoil momentum each second. Then divide by the gun's mass.

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