question_answer

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)  \[p\left( \frac{1+e}{1-e} \right)\]

Correct Answer: D

Solution :

[d] \[\Delta p=(p+ep)+(ep+{{e}^{2}}p)+({{e}^{2}}p+e{{p}^{3}})+...\] \[=p(1+e)[1+e+{{e}^{2}}+...]=\frac{p(1+e)}{(1-e)}\]