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Sir, would you please explain to me about the law of conservation of momentum.

 According to the law conservation of momentum: When two (or more bodies act upon one another, their total momentum and the remains constant (or conserved) provided no external forces are action. The law of conservation of momentum means that whenever one body gains momentum, then some other body must lose an equal amount of momentum. This law can also be stated as: Momentum is never created or destroyed. We will now take an example to prove the law of conservation of momentum. Suppose two bodies, a truck and a car, are moving in the same direction (towards) but with different speeds or velocities. Let the mass of the truck be m₁ and its velocity be u₁ so that its initial momentum is m₁u₁. Let the mass of the car be m₂ and its velocity be u₂ so that the initial momentum of the car is m₂u₂. Thus, the total momentum of the truck and the car before collision is m₁u₁ + m₂u₂.

Suppose the truck and the car collide for a short time. Due to collision, the velocities of the truck and the car will change. Let the velocity of the truck after the collision be v₁, and the velocity of the car after the collision be v₂.  So the momentum of the truck after the collision will be m₁v₁, and the momentum of the car after the collision will be m₂v₂. In this way, the total momentum of the truck and the car after the collision will be m₁v₁ + m₂v₂.

Suppose that during collision, the truck exerts a force F₁ on the car and, in turn, the car exerts a force F₂ on the truck. We will now find out the values of the forces F₁ and F₂. This can be done as follows:

(i)       When the force F₁ of the truck acts on the car for a time t, then the velocity of car changes from u₂ to v₂. So, 

But, force, mass x acceleration, so the force F₁ exerted by the truck on the car is given by :

(ii) When the force F₂ of the car reacts on the truck for a time t, then the velocity of the truck changes from u₁ to v₁. So, 

But, force = mass x acceleration, so the force F₂ exerted by car on the truck is given by:

Now, the force F1 exerted by the truck is the ‘action’ and the force F₂ exerted by the car is the ‘reaction’. But according to the third law of motion, the action and reaction are equal and opposite. That is,
F₁ = -F₂ 
Now, putting the values of F₁ and F₂ from equations (1) and (2), we get:

Cancelling t from both sides, we get :
        m₂ (v₂ – u₂) = -m₁ (v₁ – u₁)
or   m₂v₂ – m₂u₂ = -m₁v₁ + m₁u₁
or    m₂v₂ + m₁v₁ = m₂u₂ + m₁u₁
or   m₁u₁ – m₂u₂ = m₁v₁ + m₂v₂
Now, m₁u₁ + m₂u₂ represents total momentum of the truck and car before collision whereas m₁v₁ + m₂v₂ represents the total momentum of the truck and car after collision. This means that:
Total momentum before collision = Total momentum after collision
It is obvious that the total momentum of the two bodies before and after the collision is the same. This means that the momentum of the two bodies remains constant (or conserved). And this result proves the law of conservation of momentum.