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Question

Two billiard balls undergo a head-on collision. Ball 1 is twice as heavy as ball 2. Initially, ball 1 moves with a speed u towards ball 2 which is at rest. Immediately after the collision, ball 1 travels at a speed of u3 in the same direction. What type of collision has occurred?

A
Inelastic
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B
Elastic
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C
Completely inelastic
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D
cannot be determined from the information
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Solution

The correct option is B Elastic
Let mass of ball 1=2m
Mass of ball 2=m
Velocity of ball 1 before collision =u
Velocity of ball 1 after collision =u3
Velocity of ball 2 before collision =0
Let final velocity of ball 2=v2

As there is no external force on the system, momentum will be conserved.
Applying conservation of linear momentum before and after collision.
(2m)u+m(0)=(m)v2+(2m)(u3)
or v2=4u3
Now,
e=velocity of separationvelocity of approach
e=v2v1u1u2
e=4u3u3u0=1
Hence, collision is elastic.

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