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A sphere A of mass m moving with a constant velocity u hits another stationary sphere B of the same mass. If e is the coefficient of restitution, then the ratio of the velocity of A and B after collision will be:

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

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

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

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

answer is A.

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Detailed Solution

${mv}_{1} + {mv}_{2} = mu$

$v_{1} + v_{2} = u \dots (1)$

$v_{2} - v_{1} = eu \dots (2)$

$v_{1} = \frac{u}{2} (1 - e) and v_{2} = \frac{u (1 + e)}{2}$

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

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