Twelve persons are initially at 12 corners of a regular polygon of 12 sides of side a. Each person now moves with a uniform speed v in such a manner that 1 is always directed towards 2, 2 towards 3, 3 towards 4, and so on. The time after which they meet is

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$\frac{v}{a}$

$\frac{2 a}{v (2 - \sqrt{3})}$

$\frac{2 a}{v (2 + \sqrt{3})}$

$\frac{2 a}{v}$

answer is D.

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Detailed Solution

At every instant the twelve persons will make a regular polygon

$\begin{array}{l} t = \frac{a}{v - vcos \frac{π}{n}} \cdot Here n = 12 \\ \Rightarrow t = \frac{a}{v - vcos \frac{2 π}{12}} = \frac{2 a}{v (2 - \sqrt{3})} \end{array}$

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