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A sphere A of mass m moving with a velocity hits another stationary sphere B of same mass. If the ratio of the velocities of the sphere after collision is vAvB = 1-e1+e where e is the coefficient of restitution, what is the initial velocity of spheres 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--------(i)But e = vB-vAu------(ii)or u = 2evBe(1+e) ⇒ u+eu = 2vBor u + (vB-vA) = 2vB ⇒ u = vA + vB

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