Question

A sphere of mass m moving with constant velocity $\mu$ , 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 $mu=m({{v}_{1}}+{{v}_{2}})$ or ${{v}_{1}}+{{v}_{2}}=u$ ?(i) Again the coefficient of restitution is given by $e=\frac{{{v}_{2}}-{{v}_{1}}}{u}$ or ${{v}_{2}}-{{v}_{1}}=eu$ ?(ii) Solving Eqs. (i) and (ii), we get ${{v}_{1}}=\frac{u}{2}(1-e),{{v}_{2}}=\frac{u}{2}(1+e)$ Therefore, $\frac{{{v}_{1}}}{{{v}_{2}}}=\left( \frac{1-e}{1+e} \right)$