On a frictionless surface, a ball of mass m moving at a speed v makes a head on collision with an identical ball at rest. The kinetic energy of the balls after the collision is 3/4th of the original. Find the coefficient of restitution.

Explanation

As we have seen in the above discussion, that under the given conditions :

By using conservation of linear momentum and equation of e, we get,
`v_(1)'=((1+e)/(2))v and v_(2)'=((1-e)/(2))v`
Given that `K_(f)=(3)/(4)K_(1)`
or `(1)/(2)mv'_(1)^(2)+(1)/(2)mv'_(2)^(2)=(3)/(4)((1)/(2)mv^(2))`
Substituting the value, we get
`((1+e)/(2))^(2)+((1-e)/(2))^(2)=(3)/(4)`
or `e=(1)/(sqrt(2))`