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COM in Collision and Explosion

A body of mas...

Question

A body of mass m moving with velocity v suffers head on elastic collision with another body of mass 2 m at rest. The ratio of kinetic energy of the colliding body before and after collision is

A

9:1

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B

12:1

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C

16:1

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D

18:1

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Solution

The correct option is C 9:1
Ratio of kinetic energy of the body before and after the collision is given by, $\frac{v_{2}^{2}}{v_{1}^{2}} = \frac{(m_{1} + m_{2})^{2}}{(m_{1} - m_{2})^{2}}$

now $m_{1} = m, m_{2} = 2 m$

So $\frac{K E_{b e f o r e}}{K E_{a f t e r}} = \frac{(m + 2 m)^{2}}{(m - 2 m)^{2}} = 9 / 1$

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