Question

If two bodies do not stick then is it an inelastic collision.

Answer 1

If the two bodies stick together after the collision, the collision is inelastic. In an elastic collision, the total kinetic energy is the same after the collision as it was before the collision. We know that the total momentum is conserved both for elastic and inelastic collisions, and we can choose to look at the system in a reference frame where the total momentum is zero. The center of mass of the two bodies together must then be at rest all the time. That means that both the bodies will come to rest after the collision, and lose all their kinetic energy, so the total kinetic energy will not be conserved in the collision.