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A sphere of mass $m$ travelling at constant speed $v$ strike another sphere of same mass. If coefficient of restitution is $e$, then ratio of velocity of both spheres just after collision is :-
$\frac{1-e}{1+e}$
$\frac{1+e}{1-e}$
$\frac{e+1}{e-1}$
$\frac{e-1}{e+1}$
Solution
$\mathrm{V}_{1}=\frac{\mathrm{m}_{1}-\mathrm{em}_{2}}{\mathrm{m}_{1}+\mathrm{m}_{2}} \mathrm{u}_{1}+\frac{(1+\mathrm{e}) \mathrm{m}_{2}}{\mathrm{m}_{1}+\mathrm{m}_{2}} \mathrm{u}_{2}$
$\mathrm{V}_{2}=\frac{(1+\mathrm{e}) \mathrm{m}_{1}}{\mathrm{m}_{1}+\mathrm{m}_{2}} \mathrm{u}_{1}+\frac{\mathrm{m}_{2}-\mathrm{em}_{1}}{\mathrm{m}_{1}+\mathrm{m}_{2}} \mathrm{u}_{2}$
$\mathrm{m}_{1}=\mathrm{m}_{2}=\mathrm{m}, \quad \mathrm{u}_{2}=0$
$\frac{V_{1}}{V_{2}}=\frac{m-e m}{2 m} u_{1} \times \frac{m+m}{(1+e) m} \frac{1}{u_{1}}$
$\frac{V_{1}}{V_{2}}=\frac{1-e}{1+e}$
