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Question

A sphere of mass m moving with a constant velocity u hits another stationary sphere of same mass. If e is the coefficient of restitution, then ratio of velocities of the two spheres v1v2 after collision will be

A
12e1+2e
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B
1+e1e
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C
2e+12e1
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D
e1e+1
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Solution

The correct option is B 1+e1e
From conservation of linear momentum:

mu=mv1+mv2
or u=v1+v2.....(i)
From definition of e:
v1v2=eu....(ii)
Solving these two equatoins, we get
v1=(1+e2)u
and v2=(1e2)u
v1v2=(1+e1e)

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