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Question

A sphere of mass m moving with a constant velocity collides with another stationary sphere of same mass. The ratio of velocities of two spheres after collision will be, if the co-efficient of restitution is e:

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

The correct option is A 1e1+e

The law of conservation of linear momentum tells us that the overall momentum before the collision must be equal to the overall momentum after a collision.

Since the spheres have identical masses, we can write

mu+m×0=mvA+mvB

u=vA+vB

From the definition of the coefficient of restitution, we know that

e=vBvAu

solving above two equations

e×(vA+vB)=vBvA

vB(1e)=vA(1+e)

vAvB=1e1+e


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