A ball of mass m moving at a speed u makes a head-on collision with an identical ball at rest. The kinetic energy of the balls after the collision is three fourths of the original. Find the coefficient of restitution.

Mass of the first ball is m and velocity of the first ball is v.


Mass of the second ball is m,


Let the final velocities of the first ball and second ball are v1 and v2 respectively.


From law of conservation of momentum


mv1+mv2 = mv+0


v1+v2=v ----------------- (1)


v1 - v2= ev ----------------- (2)


Since, final kinetic energy = � (initial kinetic energy)






Putting values from equation (1) and (2)







So, the coefficient of restitution (e) is


1