# Velocity after collision

Let two bodies

*A*and*B*collide inelastically and coefficient of restitution is*e*.where

From the law of conservation of linear momentum,

By solving (20) and (21), we get

Similarly,

By substituting

*e*= 1, we get the value of*v*_{1}and*u*_{2}for perfectly elastic head-on collision.# Ratio of velocities after inelastic collision

A sphere of mass

*m*moving with velocity*u*hits inelastically with another stationary sphere of same mass (Fig. 7).**Fig. 7**

By conservation of momentum:

Momentum before collision = Momentum after collision

Solving (22) and (23), we get and .

âˆ´

# Loss in kinetic energy

Loss (Î”

*K*) = Total initial kinetic energy â€“ Total final kinetic energy=

Substituting the value of

*v*_{1}and*v*_{2}from the above expression,Loss (Î”

*K*) =By substituting

*e*= 1, we get Î”*K*= 0, i.e., for perfectly elastic collision, loss of kinetic energy will be zero or kinetic energy remains constant before and after the collision.