Question

A sphere of mass $m$ moving with constant velocity $u$ , collides with another stationary sphere of same mass. If $e$ is the coefficient of restitution, the ratio of the final velocities of the first and second spheres is

• A. $\frac{1+e}{1-e}$
• B. $\frac{1-e}{1+e}$
• C. $\frac{e}{1-e}$
• D. $\frac{1+e}{e}$

Answer 1

Answer: (B)

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

Answer 2

Let $v_{1}, v_{2}$ be the final velocities of the two spheres. Applying the law of conservation of linear momentum $m u=m\left(v_{1}+v_{2}\right)$ or $v_{1}+v_{2}=u \ldots$ (i) Again the coefficient of restitution is given by $e=\frac{v_{2}-v_{1}}{u}$ or $v_{1}+v_{2}=u \ldots$ (ii) Solving Eqs. (i) and (ii), we get $v_{1}=\frac{u}{2}(1-e), v_{2}=\frac{u}{2}(1+e)$ Therefore, $\frac{v_{1}}{v_{2}}=\left(\frac{1-e}{1+e}\right)$