Question

A gun of mass 500g fires a bullet of mass 10g with a speed of 100m/s.

Find:

(a) Initial momentum of ' gun + bullet ' .

(b) Momentum gained by the bullet after firing.

(c) Recoil velocity of the gun

Answer 1

Information provided in the question is as follows:

Mass of the gun, M	500 g = 0.5 kg
Mass of the bullet, m	10 g = 0.01 kg
Velocity of the bullet, v	100 m/s

As initially both the gun and the bullet are at rest so the velocity of both bullet and gun is 0.
Therefore, the initial momentum of gun and bullet, p_i = Mv_i+mv_i' = 0

Momentum gained by the bullet after firing, p = mv = 0.01×100 = 1 kg m s^-1

Let the recoil velocity of the gun be V.
From conservation of momentum,
Final momentum of the system = initial momentum of the system
MV +mv = 0
⇒0.5×V = -1
⇒V = - 1/0.5 = -2 m/s