Q. A tennis ball bounces down flight of stairs striking each step in turn and rebounding to the height of the step above. The coefficient of restitution has a value
A) $1/2$
B) 1
C) 1/$\sqrt{2}$
D) 1/2$\sqrt{2}$
Explanation
(c) As shown in adjoining figure ball is falling from height 2$h$ and rebounding to a height $h$ only. It means that velocity of ball jus before collision
$u = \sqrt{\frac{2(2h)}{g}} = \sqrt{\frac{4h}{g}}$ and velocity just after collision
[image:7_image90.jpeg]
$v = - \sqrt{\frac{2h}{g}}$
$\therefore e = \frac{- v\sqrt{\frac{2h}{g}}}{u\ \sqrt{\frac{4h}{g}\ }} = \frac{1}{\sqrt{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.