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Question

Ball 1 Collides head-on with another identical ball 2 at rest. The velocity of ball 2 after collision becomes two times to that of ball 1 after a collision. The coefficient of restitution between the two balls is

A
e=1/3
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B
e=1/2
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C
e=1/4
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D
e=2/3
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Solution

The correct option is A e=1/3
Both balls have mass 'm'.
Initially ball 1 moves with v.
After collision ball 1 moves with v2
After collision ball 2 moves with 2v2
Momentum is conserved.
i.e.
mv=mv2+2mv2=3mv2
i.e.
v2=v3
Velocity of approach =v0=v
Velocity of separation =23v13v=13v
Coefficient of restitution is velocity of approach by velocity of separation.
e=v/3v=13

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