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# A small ball on a friction less horizontal surface moves towards right with velocity V. It collides with the wall and return back and continues to and fro motion. If the average speed for first to and fro motion of the ball is $\bigg(\large\frac{2}{3} V\bigg)$, then the coefficient of restitution of impact is

$\begin {array} {1 1} (a)\;0.5 & \quad (b)\;0.8 \\ (c)\;0.25 & \quad (d)\;0.75 \end {array}$

Can you answer this question?

Velocity after collision $=eV$
Total distance $=2S$
Total time $= \large\frac{s}{V}+\frac{s}{eV}$
$v_{av}= \large\frac{2s}{s/V+3/eV}$
$\large\frac{2}{3} $$V=\bigg(\large\frac{2e}{e+1}\bigg)$$V=> e=0.5$
answered Nov 24, 2013 by
edited Jun 18, 2014