JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Conservation of Momentum

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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

. The initial speed of the smaller body before collision is ____

ms^{- 1}

Answer: 4

Solution

In a head-on elastic collision with a stationary target, the rebound speed of the incoming body is

v_{1}^{'} = \frac{m _{1} - m _{2}}{m _{1} + m _{2}} u_{1} = \frac{1 - 3}{4} u_{1} = - \frac{u _{1}}{2}

. The minus sign shows the reversal, and its size equals the given

2 m/s

, so

\frac{u _{1}}{2} = 2

. The smaller body approached at

4 m/s

JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Integer answer

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