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Final Velocities

A body of mas...

Question

A body of mass $m_{1}$ moving at a constant speed undergoes an elastic collision with a body of mass $m_{2}$ initially at rest., the ratio of the kinetic energies of masses $m_{2}$ and $m_{1}$ after the collision is

A

\frac{m_{1} m_{2}}{(m_{1} - m_{2})^{2}}

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B

\frac{\sqrt{2} m_{1} m_{2}}{(m_{1} - m_{2})^{2}}

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C

\frac{2 m_{1} m_{2}}{(m_{1} - m_{2})^{2}}

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D

\frac{4 m_{1} m_{2}}{(m_{1} - m_{2})^{2}}

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Solution

The correct option is D $\frac{4 m_{1} m_{2}}{(m_{1} - m_{2})^{2}}$
KE of $m_{2}$ afer collision = $\frac{1}{2} m_{2} v_{2}^{2} = \frac{1}{2} m_{2} {(\frac{2 m_{1}}{m_{1} + m_{2}})}^{2} u_{1}^{2}$ .
KE of $m_{1}$ afer collision = $\frac{1}{2} m_{1} v_{1}^{2} = \frac{1}{2} m_{1} {(\frac{m_{1} - m_{2}}{m_{1} + m_{2}})}^{2} u_{1}^{2}$ .
Dividing the two, we find that the correct choice is (d).

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