Question

a gun weighting 10 kg fires A bullet of 10 gram with a velocity of 330 metre per second with what velocity does the gun recoil please give the answer with full solution​

Answer 1

Mass of gun, M = 10 kg

Mass of bullet, m = 30 g = 0.03 kg

Velocity of bullet, v = 330 m/s

Velocity of gun, V = ?

Momentum of the system (gun and bullet) before firing = 0

Momentum of the system (gun and bullet) after firing = mv + MV

Using conservation of momentum,

mv + MV = 0

=> 0.03 × 330 + 10V = 0

=> V = -0.99 m/s

(the negative sign implies direction of velocity of gun is opposite to that of the bullet)

Momentum of the gun after firing = MV = 10 × (-0.99) = -9.9 kg m/s

Momentum of the bullet after firing = mv = 0.03 × 330 = 9.9 kg m/s

Note that the momentum of the bullet and the gun are equal and opposite after firing.

Before firing the gun and bullet were at rest hence no momentum before firing.

Both before and after firing the momentum of gun and bullet together is zero.