Work Energy And Power Question 319
Question: Two identical billiard balls are in contact on a table. A third identical ball strikes them symmetrically and comes to rest after impact. The coefficient of restitution is
Options:
A) $ \frac{2}{3} $
B) $ \frac{1}{3} $
C) $ \frac{1}{6} $
D) $ \frac{\sqrt{3}}{2} $
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Answer:
Correct Answer: A
Solution:
[a] $ \sin \theta =\frac{r}{2r}=\frac{1}{2}\Rightarrow \theta =30{}^\circ $
From conservation of linear momentum,
$ mu=2mv\cos 30{}^\circ orv=\frac{u}{\sqrt{3}} $
Now $ e=\frac{Relativevelocityofseparation}{Relativevelocityofapproch} $
(in common normal direction)
Hence, $ e=\frac{v}{u\cos 30{}^\circ }=\frac{u/\sqrt{3}}{u\sqrt{3}/2}=\frac{2}{3} $
