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# 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 balls after the collision is 34th of the original. If e is the coefficient of restitution. Then:

A
After collision, ball which was initially at rest starts moving with velocity 1+122v
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B
After collision, ball which was initially moving, has velocity 1122v
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C
e=12
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D
e=12
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Solution

## The correct option is C e=1√2Given that a ball of mass m moving at a speed v makes a head on collision with an identical ball at rest. For e=velocity of seperationvelocity of approach e=v2−v1v−0 v2−v1=ev....(1) now from conservation of linear momentum, mv=mv1+mv2 v=v1+v2.....(2) From (1)(2), we get v1=(1−e2)v and v2=(1+e2)v Given that, 34KEi=KEf ⇒34(12mv2)=12m{(1−e2)v}2+12m{(1+e2)v}2 ⇒34=(1−e)24+(1+e)24 ⇒3=2+2e2 ⇒1=2e2 ∴e=1√2 and v1=⎛⎜ ⎜ ⎜ ⎜⎝1−1√22⎞⎟ ⎟ ⎟ ⎟⎠v  Suggest Corrections  0      Similar questions
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