**What is the law of conservation of momentum?**

**OR**

**State and explain the law of conservation of momentum?**

Difficulty: Hard

**Law of conservation of momentum:**

The momentum of an isolated system of two or, more two interacting bodies remains constant.

**Example:**

Consider the example of an air-filled balloon as described under the third law of motion. In this case, the balloon and the air inside it form a system. Before releasing the balloon, the system was at rest and hence the initial momentum of the system was zero. As soon as the balloon is set free, air escapes out of it with some velocity. The air coming out of it possesses momentum. To conserve momentum, the balloon moves in a direction opposite to that of air rushing out.

**Explanation: **

Law of conservation of momentum applies to all objects in the universe. A rocket and jet engine are taking off. The recoil of a gun is an example that demonstrates the importance of the law of conservation of momentum.

**Case I:**

Consider an isolated system of two spheres of masses m_{1} and m_{2}. They are moving in a straight line with initial velocities u_{1} and u_{2} respectively such that u_{1} is greater than u_{2}. The sphere of mass m_{1} approaches the sphere of mass m_{2} as they mThe initial

The initial momentum of mass m_{1} =m_{1}u_{1}

The initial momentum of mass m_{2} =m_{2}u_{2}

**The total initial momentum of the system before collision = m _{1}u_{1}+m2u2 ………(i)**

**Case II:**

After sometimes mass m_{1} hit m_{2} with some force. According to newton's third law of motion, m_{2} exerts an equal and opposite reaction force on m_{1}. Let their velocities become v_{1} and v_{2} respectively after the collision. Then

Final momentum of mass m_{1} = m_{1}u_{1}

Final momentum of mass m_{2} = m_{2}u_{2}

**Total final momentum of the system before collision = m _{1}u_{1}+m_{2}u_{2} ………(ii)**

** **

**According to the Law of conservation of momentum:**

[ total initial momentum of the system before collison] = [ total initial momentum of the system before system]

**m _{1}u_{1} + m_{2}u_{2} = m_{1}v_{1} + m_{2}v_{2}......... (iii)**

Equation (iii) shows that the momentum of an isolated system before and after collisions remains the same which is the law of conservation of momentum. The Law of conservation of momentum is important and has vast applications.

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