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Q.

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

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a

$p (1 + e)$

b

$\frac{p}{1 - e}$

c

$p (\frac{1 - e}{1 + e})$

d

$p (\frac{1 + e}{1 - e})$

answer is D.

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Detailed Solution

$\begin{array}{l} Δ P_{1} = (1 + e) P \\ Δ P_{2} = (1 + e) e P \end{array}$

And so on,

Question Image

$\begin{matrix} Δ P_{Total} = Δ P_{1} + Δ P_{2} \\ = (1 + e) P (1 + e + e^{2} + \dots) \\ = (\frac{1 + e}{1 - e}) P \end{matrix}$

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