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  4. 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 ((v1/v2)) will be

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Q. 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 $\left(\frac{v_{1}}{v_{2}}\right)$ will be

ManipalManipal 2016

Solution:

Conservation of momentum (gives)
$m u+0=m v_{1}+m v_{2}$
$\Rightarrow v_{1}+v_{2}=u$ ...(i)
Newton's experimental formula,
$v_{1}-v_{2}=-e\left[u_{1}-u_{2}\right]$ gives
$v_{1}-v_{2}=-e u$ ...(ii)
From Eqs. (i) and (ii), we get
$v_{1}=\frac{(1-e) u}{2}$
$v_{2}=\frac{(1+e) u}{2}$
$\therefore \frac{v_{1}}{v_{2}}=\frac{1-e}{1+e}$