A ball A moving with a certain velocity collides, with another ball B of the same mass at rest. If the coefficient of restitution is e, the ratio of the velocities of A and B just after the collision is

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$\frac{1 + e}{1 - e}$

$\frac{1 + e}{2}$

$\frac{1 - e}{2}$

$\frac{1 - e}{1 + e}$

answer is D.

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Detailed Solution

$m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2}$

$m u_{1} = m_{1} v_{1} + m v_{2}$

$u_{1} = v_{1} + v_{2} \to$ ……… (1)

$e = \frac{v_{2} - v_{1}}{u_{1} - 0} \Rightarrow e u_{1} = v_{2} - v_{1}$ …….(2)

Solving (1) and (2)

$v_{1} = \frac{1 - e}{2}$ $v_{2} = \frac{1 + e}{2}$

$\frac{v_{1}}{v_{2}} = \frac{1 - e}{1 + e}$

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