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Q.

A body of mass m₁ moving at a constant speed undergoes an elastic collision with a body of mass m₂ initially at rest. the ratio of the kinetic energies. of masses m₂ and m₁ after the collision is

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a

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

b

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

c

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

d

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

answer is D.

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Detailed Solution

$K E o f m_{2}$ after 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 $m_{1}$ after 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 ( 4).

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