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A particle of mass $m$ is moving along the x-axis with speed $v$ when it collides with a particle of mass $2 m$ initially at rest. After the collision, the first particle has come to rest and the second particle has split into two equal-mass pieces that are shown in the figure. Which of the following statements correctly describes the speeds of the two places? $(θ > 0)$

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Each piece moves with speed $v$

Each piece moves with speed $v / 2$

One of the pieces moves with speed $v / 2,$ the other moves with speed greater than $v / 2$

Each piece moves with speed greater than $v / 2$

answer is D.

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Detailed Solution

After collision by momentum conservation:

Along y-axis: $0 = 0 + m v_{2} \sin θ - m v_{3} \sin θ \Rightarrow v_{2} = v_{3}$

Along x-axis: $m v = 0 + m v_{2} \cos θ + m v_{3} \cos θ$

$m v = 2 m v_{2} \cos θ$

$v_{2} = \frac{v}{2} \frac{1}{\cos θ}$ so $v_{2} = v_{3} > \frac{v}{2}$

$∵ \cos θ < 1$

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