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Question

A particle of mass 3 kg moving with a velocity of 6^i m/s collides head on with another particle of mass 5 kg moving with a velocity of 2^i m/s. If after the collision, first particle has a speed of 1 m/s along the negative X axis, find the coefficient of restitution.

A
0.4
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B
0.5
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C
0.6
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D
0.3
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Solution

The correct option is A 0.4
Given,
Mass of first particle, m1=3 kg
Mass of second particle, m2=5 kg
Let u1 & u2 be the initial velocity of 1st and 2nd particle respectively.
v1 & v2 be the final velocity of 1st and 2nd particle respectively.

Applying conservation of momentum before and after collision.
m1u1+m2u2=m1v1+m2v2
3×6+5×(2)=3×(1)+5v2
v2=115^i=2.2^i m/s

Coefficient of restitution e=velocity of separationvelocity of approach
e=v2v1u1u2=2.2(1)6(2)
=3.28=0.4
e=0.4
The correct option is (a).

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