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Q.

A sphere A of mass m moving with a velocity, hits another stationary sphere B of different mass. If the ratio of the velocities of the spheres after collision is VAVB=1−e1+e,  where e is the coefficient of restitution, what is the initial velocity of sphere A with which it strikes?

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a

VA+VB

b

VA−VB

c

VB−VA

d

(VA+VB)2

answer is A.

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Detailed Solution

VAVB=1−e1+e  ,VAVB−1=1−e1+e−1 Or VB−VA=2e1+e.VB                     But e=VB−VAu Or  u=2eVBe(1+e)                Or u+eu=2VB u+(VB−VA)=2VB     u=VA+VB
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