Question

If one sphere collides head-on with another sphere of the same mass at rest inelastically. The ratio of their speeds $\left(\frac{v_{2}}{v_{1}}\right)$ after collision shall be

• A. $\frac{\left(1 - e\right)}{\left(1 + e\right)}$
• B. $\frac{2 e}{\left(1 + e\right)}$
• C. $\frac{\left(1 + e\right)}{\left(1 - e\right)}$
• D. $e$

Answer 1

Answer: (C)

$v_{1}=\frac{\left(m - e m\right) u + 0}{2 m}$
$v_{2}=\frac{0 + m u \left(1 + e\right)}{2 m}$
$\therefore \, \, \, \frac{v_{1}}{v_{2}}=\frac{\left(1 - e\right)}{\left(1 + e\right)}$ ......... $\left(C\right)$
$\frac{v_{2}}{v_{1}}=\frac{\left(1 + e\right)}{\left(1 - e\right)}$