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Question

Two masses, 2m and m are moving in opposite directions, with velocities 2v and v respectively. After collision, mass 2m comes to rest and mass m moves with 3v. What are the kinetic energies of the two masses, 2m and m respectively after collision and the coefficient of restitution(e) ?

A
0, 92mv2, e=1/3
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B
0, 92mv2, e=1
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C
0, 92mv2, e=0
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D
None of the above
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Solution

The correct option is B 0, 92mv2, e=1
According to conservation of momentum principle,

2m(2v)+m(v)=2m(0)+m(v2)

v2=3v>0

This means after collision, mass m starts moving in the initial direction (before collision) as of mass 2m.

Now,

For 2m, KEf=12(2m)(0)2=0

For m, KEf=12(m)(3v)2=9mv22

And coefficient of restitution is,

e=v2v1u1u2=3v02v(v)=1

Hence, option (B) is the correct answer.

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