Question

A ball falls vertically onto a floor with momentum $p$, and then bounces repeatedly. If the coefficient of restitution is $e$, then the total momentum imparted by the ball on the floor till the ball comes to rest is

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

Answer 1

Answer: (D)

$ \Delta p =(p+e p)+\left(e p+e^{2} p\right)+\left(e^{2} p+e^{3} p\right)+\cdots $
$=p(1+e)\left[1+e+e^{2}+\cdots\right]=\frac{p(1+e)}{1-e} $