A ball of mass m moving at a speed y 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 co-efficient of restitution

A ball of mass m moving at a speed y makes a head on collision with an

1.	A ball of mass m moving at a speed y 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 co-efficient of restitution
Answer» Solution : `v_(1). =((1 + E )/( 2 ) ) V and v _(2) . =((1 -e )/( 2) ) v and K _(f) = 3/4 K _(i) (or) (1)/(2) mv _(1) ^(2) + (1)/(2) mv _(2) ^(.2) = (3)/(4) ((1)/(2/( mv ^(2))` Substituting the values of `v _(1). v _(2).` we GET `((1+e)/( 2 )) ^(2) + (1-e )/(2) ^(2) = 3/4` or `(1+e) ^(2) + (1-e) ^(2)=3 or 2 + 2e ^(2) = 3 (or) e ^(2) = 1/2 IMPLIES e = (1)/(sqrt2)`