Explain the total linear momentum is conserved in an elastic collision and also explain the inelastic collision and completely elastic collision.

In all collisions the total linear momentum is conserved that means the initial momentum of the system is equal to the final momentum of the system.

When two objects collide, the mutual impulsive forces acting over the collision time $\Delta t$ cause a change in their respective momenta Change in initial momentum,

$\Delta \overrightarrow{p_{1}}=\overrightarrow{F_{12}} \Delta t$

and change in final momentum,

$\Delta \overrightarrow{p_{2}}=\overrightarrow{\mathrm{F}_{2 \mathrm{l}}} \Delta t$

where $\overrightarrow{\mathrm{F}_{12}}$ is the force exerted on the first particle by the second particle. $\overrightarrow{\mathrm{F}_{21}}$ is the force exerted on the second particle by the first particle.

From Newton's third law,

$\overrightarrow{\mathrm{F}_{12}}=-\overrightarrow{\mathrm{F}_{21}}$

$\therefore \Delta \overrightarrow{p_{1}}=-\Delta \overrightarrow{p_{2}}$

$\therefore \Delta \overrightarrow{p_{1}}+\Delta \overrightarrow{p_{2}}=0$

Hence, on a system change in initial momentum is equal to change in final momentum. Elastic collision : Collision in which the total linear momentum and total kinetic energy is conserved then this collision is known as elastic collision. It is true for conservative force.

Inelastic Collisions : Collision in which the total linear momentum is conserved but kinetic energy is not conserved then this collision is known as inelastic collision. This is for nonconservative force.

Completely Inelastic Collision : A collision in which the two particles move together after the collision is called a completely inelastic collision.

Here in every collision total energy and momentum is conserved.