Question

A gun of mass M fires a bullet of mass m with a KE E. the velocity of recoil of gun is

Answer 1

Momentum before firing = 0 
Momentum after firing = mv + MV

According to law of conservation of momentum, 

mv + MV = 0
Recoil velocity V = - mv /M

Answer 2

Initial momentum before firing is 0. The momentum changes after firing = mv + MV. As per the conservation of momentum law, mv + MV = 0.

The recoil velocity V = -mv/M.

The total work carried out is equal to change in kinetic energy F.S = ½ M * v1^2; F. v1/4 = ½ M * v1^2. Thus, F = 2 Mmv / (m+M).