Ball P of mass m moving with velocity ' v ' collides with another ball Q of mass 2 m , at rest. If v P and v Q are the final velocities of P and Q respectively, after collision, then (Assume the coefficient of restitution is 1 / 3 )

Question

Ball P of mass m moving with velocity ' v ' collides with another ball Q of mass 2 m , at rest. If v P and v Q are the final velocities of P and Q respectively, after collision, then (Assume the coefficient of restitution is 1 / 3 ), v Q v P = 4, v P v Q = 4, v Q v P = 2, v P v Q = 2

MARKS App · Accepted Answer

From conservation of linear momentum, we have m v + 2 m × 0 = m v P + 2 m v Q ⇒ v = v P + 2 v Q . . . 1 From coefficient of restitution formula, we have e = 1 3 = v Q - v P v - 0 ⇒ v Q - v P = v 3 . . . 2 On dividing 1 by 2 , we have ⇒ v P + 2 v Q v Q - v P = 3 ⇒ 1 + 2 V Q v P v Q v P - 1 = 3 ⇒ 1 + 2 V Q v P = 3 v Q v P - 1 ⇒ 1 + 2 V Q v P = 3 v Q v P - 3 ⇒ V Q v P = 4

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