Q. A ball of mass $m$ moving with a velocity $u$ collides head on with another ball of mass $m$ initially at rest. If the coefficient of restitution be $e$ then the ratio of the final and initial velocities of the first ball is
A) $\frac{1 - e}{1 + e}$
B) $\frac{1 + e}{1 - e}$
C) $\frac{1 + e}{2}$
D) $\frac{1 - e}{2}$
Explanation
(d) Here $m_{1} = m_{2} = m,u_{1} = u$ and $u_{2} = 0$
$\therefore\ \ v_{1} = u_{1}\frac{(m_{1} - em_{2})}{(m_{1} + m_{2})} + u_{2}\frac{(1 + e)m_{2}}{(m_{1} + m_{2})} = \frac{u(1 - e)}{2}$
$\Rightarrow \ \ \frac{v_{1}}{u} = \left( \frac{1 - e}{2} \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.