Question

A $1.0 \, kg$ ball drops vertically into a floor from a height of $25 \, cm$ . It rebounds to a height of $4 \, cm$ . The coefficient of restitution for the collision is

• A. $0.16$
• B. $0.32$
• C. $0.40$
• D. $0.56$

Answer 1

Answer: (C)

Initial velocity before colliding floor $u=\sqrt{2 g h}$
$u=\sqrt{5}$
final velocity after colliding floor $v=\sqrt{2 g h ′}$
$v=\sqrt{0.8}$
We know that coefficient of restitution $e=\frac{v}{u}$
$e=\frac{\sqrt{0 . 8}}{\sqrt{5}}=0.4$