Question

a gun of mass 1000 kg fires a shell of mass 2kg with the velocity of 200 m per second calculate the velocity of recoil of the gun

Answer 1

Mass of gun is, mg = 1000 kg

Mass of shell, ms = 2 kg

Velocity of the shell, vs = 200 m/s

Recoil velocity of the gun is say v 

Now, momentum of the system before firing = 0 [since all were at rest]

Momentum of the system after firing = (2)(200) + (1000)(V) = 400 + 1000V

By law of conservation of momentum,

400 + 1000V = 0

=> V = -0.4 m/s

[the negative sign indicates that velocity of gun is opposite to the velocity of the shell]

Answer 2

since no external force acts on the system of gun and shell  

thus linear momentum will be conserved  

1000*v+2*200=0+0

v=-0.4 m/s