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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 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 options are
A After collision, ball which was initially at rest starts moving with velocity 1+122v
B After collision, ball which was initially moving, has velocity 1122v
C e=12
Given 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=v2v1v0
v2v1=ev....(1)
now from conservation of linear momentum,
mv=mv1+mv2
v=v1+v2.....(2)
From (1)(2), we get
v1=(1e2)v and v2=(1+e2)v

Given that, 34KEi=KEf
34(12mv2)=12m{(1e2)v}2+12m{(1+e2)v}2
34=(1e)24+(1+e)24
3=2+2e2
1=2e2
e=12
and v1=⎜ ⎜ ⎜ ⎜1122⎟ ⎟ ⎟ ⎟v

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