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Ball A of mass m moving with velocity v collides head-on with a stationary ball B of mass m .If e be the coefficient of restitution, then which of the following statments are correct

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The ratio of velocities of balls A and B after the collision is $\frac{(1 + e)}{(1 - e)}$

The ratio of the final and initial velocities of ball A is $\frac{(1 - e)}{2}$

The ratio of the velocities of balls A and B after the collision is $\frac{(1 - e)}{(1 + e)}$

The ratio of the final and initial velocities of ball B is $\frac{(1 + e)}{2}$

answer is W.

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Detailed Solution

$V_{1} = (\frac{m_{1} - e m_{2}}{m_{1} + m_{2}}) u_{1} + \frac{m_{2} (1 + e) u_{2}}{m_{1} + m_{2}}$

$V_{2} = (\frac{m_{2} - e m_{1}}{m_{1} + m_{2}}) u_{2} + \frac{m_{1} (1 + e) u_{1}}{m_{1} + m_{2}}$

$u_{2} = 0, m_{1} = m_{2} = m$

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