Suggest some of the examples for laws of conservation of momentum?

Law of Conservation of Momentum states that: For two or more bodies in an isolated system acting upon each other, their total momentum remains constant unless an external force is applied. Therefore, momentum cannot be changed without an external force.

Example 1st- System of Gun and Bullet

In a system of gun and a bullet, before firing the gun, both the gun and the bullet are at rest, so the total momentum of the system is zero. As the gun is fired, bullet shoots out of the gun and acquires momentum. To conserve the momentum of the system, the gun recoils. According to the law of conservation of momentum, the total momentum of the gun and the bullet will be zero after the gun is fired.

Let m be the mass of the bullet and v be the velocity on firing the gun; M is the mass of the gun and V be the velocity with which it recoils. Thus the total momentum of the gun and the bullet after the gun is fired will be:

The total momentum of gun and bullet after the gun is fired = M V + mv …......(1)

According to the  conservation of momentum law:

The total momentum of gun and bullet after the gun is fired =Total momentum of gun and bullet before the gun is fired

Therefore we get:

M V + mv = 0 or M V = -mv

Example 2nd - System of Air and Balloon

In a system of an air-filled balloon, the balloon and the air inside it form a system. Before releasing the balloon, the system was at rest and therefore the initial momentum of the system was zero. As soon as the balloon is released, air escapes out of it possesses momentum. To conserve momentum, the balloon moves in a direction opposite to that of air rushing out.