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Perfectly Elastic Collision

A particle of...

Question

A particle of mass $m_{1}$ moving with a velocity of $5 m / s$ collides head on with a stationary particle of mass $m_{2}$ . After collision both the particle move with a common velocity of $4 m / s$ , then the value $m_{1} / m_{2}$ is:

4:1

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2:1

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1:8

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1:2

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Solution

The correct option is A 4:1
Conservation of Momentum principle,
Initial momentum is $M_{i} = 5 m_{1}$
Final momentum is $M_{f} = 4 (m_{1} + m_{2})$
By the above stated principle $M_{i} = M_{f} = 5 m_{1} = 4 (m_{1} + m_{2})$
$⟹ m_{1} = 4 m_{2}$
$∴ m_{1} : m_{2} = 4 : 1$

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