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Question

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 three fourths of the original. Find the coefficient of restitution.

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Solution

Mass of 1st ball=m and speed =v Mass of 2nd ball =m
Let final velocities of 1st and 2nd ball are v1 and v2 respectively Using law of conservation of momentum,
m(v1+v2) =mv
v1+v2 =v ...(i)
Also
v1v2=ev ....(ii)
Given that
final K.E. = 34 Initial K.E.
12 mv21 + 12 mv22 = 34× 12mv2
v21+v22= 34v2
(v1+v2)2+(v1v2)22 = 34v2
(1+e2)2v2=34v2
1+e2=34
e2=12
e=12

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