When 2 bodies collide each other then the sum of momentum before collision and after collision must be equal

The Law of Conservation of Momentum states that the total momentum of a closed system remains constant if no external forces act on it. In other words, the momentum before an event is equal to the momentum after the event, as long as there are no external forces involved.

Explanation:

What is momentum?
Momentum is a property of moving objects and is defined as the product of an object's mass and its velocity. Mathematically, momentum (p) can be expressed as p = m * v, where m is the mass of the object and v is its velocity.

Conservation of momentum in an isolated system:
An isolated system refers to a collection of objects that do not interact with any external forces. When there are no external forces acting on a system, the total momentum of the system remains constant. This means that if two objects collide and exert forces on each other, their total momentum before the collision will be equal to their total momentum after the collision.

Impulse and momentum:
Impulse is the change in momentum of an object and is equal to the force applied to the object multiplied by the time interval over which the force is applied. Mathematically, impulse (J) can be expressed as J = F * Δt, where F is the force and Δt is the time interval.

Newton's third law of motion:
According to Newton's third law of motion, for every action, there is an equal and opposite reaction. This means that when two objects interact, the forces they exert on each other are equal in magnitude and opposite in direction.

Applying the law of conservation of momentum:
When two objects interact, the total momentum before the interaction is equal to the total momentum after the interaction if no external forces are involved. This can be explained by the fact that the change in momentum of one object due to the force exerted by the other object is equal in magnitude and opposite in direction. Therefore, the total change in momentum is zero, resulting in the conservation of momentum.

Real-life examples:
- When a car collides with another car and comes to a stop, the total momentum before the collision is equal to the total momentum after the collision, even though the individual momenta of the cars may change.
- When a person jumps off a boat, the boat moves in the opposite direction with a momentum equal to the person's momentum, ensuring the conservation of momentum.

Conclusion:
The Law of Conservation of Momentum is a fundamental principle in physics that describes the behavior of momentum in isolated systems. It states that the total momentum of a closed system remains constant if no external forces act on it. This law has various applications in understanding the motion and interactions of objects, from collisions to rocket propulsion.