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 velocities of the two spheres after collision $(\frac{v_{1}}{v_{2}})$ will be :

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

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

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

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

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Solution

The correct option is C $\frac{1 - e}{1 + e}$
Conservation of momentum (gives)
$m u + 0 = m v_{1} + m v_{2}$
$\Rightarrow v_{1} + v_{2} = u . . . . (i)$
Newton's experimental formula.
$v_{1} - v_{2} = - e [u_{1} - u_{2}] g i v e s$
$v_{1} - v_{2} = - e u . . . . (i i)$
From Eqs. (i) and (ii), we get
$v_{1} = \frac{(1 - e) u}{2}$
$v_{2} = \frac{(1 + e) u}{2}$
$∴ \frac{v_{1}}{v_{2}} = \frac{1 - e}{1 + e}$ .

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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 velocities of the two spheres after collision (v1v2) will be :

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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 velocities of the two spheres after collision $(\frac{v_{1}}{v_{2}})$ will be :