A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 m/s, what is the recoil speed of the gun?

Ques: A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 m/s, what is the recoil speed of the gun? 

Ans: Mass of the gun, M = 100 kg

Mass of the shell, m = 0.020 kg

Muzzle speed of the shell, v = 80 m/s

Recoil speed of the gun = V

Both the gun and the shell are at rest initially.

Initial momentum of the system = 0

Final momentum of the system = m v – MV

Here, the negative sign appears because the directions of the shell and the gun are

opposite to each other.

According to the law of conservation of momentum:

Final momentum = Initial momentum

m v – MV = 0

V = m v / M

   = 0.20 × 80 / 100 × 1000

   = 0.016 m/s