Conservation of momentum is used by particle physicists to understand the decay

Question

Conservation of momentum is used by particle physicists to understand the decay of unstable particles. Suppose that you have a particle with mass of 3m that is initially stationary. This particle undergoes decay, releasing two particle. The first particle has mass m and moves to the left with speed v. The second particle has mass 2m. Based on conservation of momentum, which of the following statements must be true?

Answer choices:

A. The second particle moves the right with speed v/2

B. The second particle is stationary

C.The second particle moves to the left with speed v

D. The second particles moves to the right with speed 2v

Explanation / Answer

[A]

From the conservation of momentum,

Initial momentum = final momentum.

Initially, the 3m mass particle is at rest (velocity=0). so, the momentum (mass x velocity) is zero.

therefore, final momentum = 0

implies, the sum of momentums of both particles is 0.

so, both have the same momentum but in opposite directions.

Since the mass "m" is having velocity "v" (momentum = mv)

the mass "2m" should have velocity "v/2" but in opposite direction i.e., towards right

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