A sphere of mass m moving with velocity v collides head-on with another sphere of the same mass at rest. If the coefficient of restitution e = 1 2 , then what is the ratio of final velocity of the second sphere to the initial velocity of the first sphere?

Question

A sphere of mass m moving with velocity v collides head-on with another sphere of the same mass at rest. If the coefficient of restitution e = 1 2 , then what is the ratio of final velocity of the second sphere to the initial velocity of the first sphere?,

MARKS App · Accepted Answer

mv + 0 = mv 1 + mv 2 v 1 + v 2 = v ....(i) e = v 2 − v 1 v − 0 ev = v 2 − v 1 ..(ii) Add equation (i) & equation (ii) ev + v = 2 v 2 v 2 = v ( e + 1 ) 2 v 2 v = e + 1 2 = 0 . 75

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