| Two particles A and B of equal mass M are moving with the same speed \[\upsilon \] as shown in the figure. |
| They collide completely in elastically and move as a single particle C. The angle \[\theta \] that the path of C makes with the X-axis is given by [JEE Online 09-04-2017] |
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A) \[\tan \theta \,=\frac{\sqrt{3}-\sqrt{2}}{1-\sqrt{2}}\]
B) \[\tan \theta \,=\frac{1-\sqrt{2}}{\sqrt{2}(1+\sqrt{3})}\]
C) \[\tan \theta \,\frac{1-\sqrt{3}}{1+\sqrt{2}}\]
D) \[\tan \theta \,=\frac{\sqrt{3}+\sqrt{2}}{1-\sqrt{2}}\]
Correct Answer: D
Solution :
| [d] \[2mv'\,\sin \theta \,=\frac{mv}{\sqrt{2}}+\frac{mv\sqrt{3}}{2}\] |
| \[3\,mv'\,\cos \theta \,=\frac{mv}{2}\,-\frac{mv}{\sqrt{2}}\] |
| \[\sin \theta \,\frac{\frac{1}{\sqrt{2}}\,+\frac{\sqrt{3}}{2}}{\frac{1}{2}-\frac{1}{\sqrt{2}}}\] |
| \[=\frac{\sqrt{2}+\sqrt{3}}{1-\sqrt{2}}\] |
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