JEE Main & Advanced Physics Work, Energy, Power & Collision / कार्य, ऊर्जा और शक्ति Sample Paper Topic Test - Work Energy Power

  • question_answer
    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

    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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