A sphere of mass 'm' moving with a constant velocity 'u' hit

Question

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

Options:

A . 1−e1+e

B . 1+e1−e

C . e+1e−1

D . e+1e−1t2

Answer: Option A
:
A
Let the final velocities of the two masses be

v_{1}

and

v_{2}

By definition,

e = \frac{v_{2} - v_{1}}{0 - 4}

Conservation of linear momentum,

m (u) + 0 = m v_{1} + m v_{2}

\Rightarrow v_{1} + v_{2} = 4

∴ \frac{v_{1} + v_{2}}{v_{2} - v_{1}} = \frac{4}{- e 4}

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

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

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

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