$A$ bullet of mass $m$ is fired from a gun of mass $M$. If the velocity of the bullet is $v$,derive an expression for the recoil velocity of the gun. On which principle is this based?

(N/A) When a bullet is fired from a gun,the gun experiences a backward jerk,which is known as the recoil of the gun.
This phenomenon is based on the Law of Conservation of Momentum.
According to this law,if no external force acts on a system,the total momentum of the system remains conserved.
Initially,both the gun and the bullet are at rest,so the initial momentum of the system is $0$.
Let $m$ be the mass of the bullet,$v$ be the velocity of the bullet,$M$ be the mass of the gun,and $V$ be the recoil velocity of the gun.
According to the law of conservation of momentum:
Initial Momentum = Final Momentum
$0 = mv + MV$
$MV = -mv$
$V = -\frac{mv}{M}$
The negative sign indicates that the direction of the recoil velocity of the gun is opposite to the direction of the bullet's velocity.