The coefficient of restitution e for a perfectly inelastic collision is:
The Coefficient of Restitution is a measure of the "bounciness" of a collision between two objects: how much of the kinetic energy remains for the objects to rebound from one another vs. how much is lost as heat, or work done deforming the objects.
The coefficient, e is defined as the ratio of relative speeds after and before an impact, taken along the line of the impact:
e=Speed of separationSpeed of approach
The bodies stick together in perfectly inelastic collision and move together hence velocity of separation is zero.
(i) For perfectly elastic collision e=1
(ii) For perfectly inelastic collision e=0
(iii) For other collision 0<e<1