A) \[\frac{2}{3}\]
B) \[\frac{1}{3}\]
C) \[\frac{1}{6}\]
D) \[\frac{\sqrt{3}}{2}\]
Correct Answer: A
Solution :
[a] \[\sin \theta =\frac{r}{2r}=\frac{1}{2}\Rightarrow \theta =30{}^\circ \] |
From conservation of linear momentum, |
\[mu=2mv\,\,\cos 30{}^\circ \,\,\text{or}\,\,v=\frac{u}{\sqrt{3}}\] |
Now \[e=\frac{\text{Relative}\,\,\text{velocity}\,\,\text{of}\,\,\text{separation}}{\text{Relative}\,\,\text{velocity}\,\,\text{of}\,\,\text{approch}}\] |
(in common normal direction) |
Hence, \[e=\frac{v}{u\,\cos 30{}^\circ }=\frac{u/\sqrt{3}}{u\sqrt{3}/2}=\frac{2}{3}\] |
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