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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 2m 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 pieces ? $(θ > 0)$

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Each piece may move with speed 2v

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 A, 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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