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JEE Main202325 Jan 2023Evening ShiftPhysicsCenter of Mass, Momentum and CollisionActual

A body of mass 1 kg collides head on elastically with a stationary body of mass 3 kg . After collision, the smaller body reverses its direction of motion and moves with a speed of 2 m s - 1 . The initial speed of the smaller body before collision is ______ m s - 1 .

Correct answer

0

Step-by-step solution

Let u 1 be the initial speed of the smaller body before collision. Let v be the final speed of the bigger body after collision. Applying conservation of linear momentum, 1 × u 1 + 0 = - 2 + 3 v ⇒ u 1 = - 2 + 3 v         . . . 1 We know, coefficient of restitution for elastic perfectly collision is 1 . ⇒ 1 = v + 2 u 1 ⇒ v + 2 = u 1         . . . 2 Equating 1   and   2 , we have u 1 = 4   m   s - 1 .

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