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Two particles are moving round concentric circular paths of radii $$r_1$$ and $$r_2$$ ($$r_2 = 3r_1$$) and are closest to each other at a certain moment. The particle on the outer path has slower speed $$v_2$$ as compared to the inner one which has a speed $$v_1$$ ($$v_1 = 2v_2$$). Find the least time interval between their successive appearances at their initial positions at the same time.
Correct Answer: 0
PLACEHOLDER ANSWER - the answer is an expression. The inner particle's period is $$T_1 = \frac{2\pi r_1}{v_1} = \frac{\pi r_1}{v_2}$$ and the outer particle's is $$T_2 = \frac{2\pi (3r_1)}{v_2} = \frac{6\pi r_1}{v_2}$$. Since $$T_2 = 6T_1$$, both are back at their starting points together after the LCM of the periods. The least interval is $$T_2 = \frac{6\pi r_1}{v_2}$$.
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