A sphere of mass m moving with a constant velocity u hits another stationary sphere of same mass. If e is the coefficient of restitution, then ratio of velocities$\frac{v_2}{v_1}$ of the two spheres after collision will be

 

$\begin{array}{l}\text{Applying conservation of linear momentum}\\ mu=m{v}_1+m{v}_2\\ u=v_1+v_2\mathrm{......}\left(1\right)\\ The\text{ coefficient of restitution }\\ e=\frac{v_1-v_2}{u}\mathrm{.......}\left(2\right)\\ \text{Solving these two equations, we get}\\ {\text{ v}}_1=\left(\frac{1+e}{2}\right)u\\ v_2=\left(\frac{1-e}{2}\right)u\\ \therefore \frac{v_2}{v_1}=\frac{1-e}{1+e}\end{array}$