A collision in which the linear momentum is saved, but a part of kinetic energy change into the other forms is known the inelastic collision. In different words, the kinetic energy is not conserved. In this, the particles do not gain their size and shape completely after collision. Some fraction of mechanical power is kept by the colliding bodies in the form of deformation potential energy. However, in the absence of external tensions, law of conservation of linear momentum still holds good.
Let two objects of masses m1 and m2 moving with initial velocities 
and 
Collide and travel with velocities 
and 
respectively after the collision. By relation of linear momentum
and by conservation of kinetic energy, 
Where E is the part of energy which modifies into the useless form due to inelastic collision;
For example, if two particles coalesce after collision and the combined system travel with a velocity 
after the collision in same position, then
And loss in kinetic energy, 
or 
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