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You are supplied with three identical rods of same length and mass. If the length of each rod is 2 $π$ . Two of them are converted into rings and then placed over the third rod as shown in figure. If point A is considered as origin of the coordinate system, the coordinates of the centre of mass will be (you may assume AB as X-axis of the coordinate system)

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$(π, \frac{1}{3})$

$(\frac{π}{2}, \frac{2}{3})$

$(π, \frac{2}{3})$

$(\frac{π}{2}, \frac{1}{3})$

answer is D.

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Detailed Solution

Here, $2 πR = 2 π \Rightarrow R = 1$

$∴ y_{CM} = \frac{m \times 0 + m \times 1 + m \times 1}{m + m + m} = \frac{2}{3}$

and $x_{C M} = \frac{m (π) + m (0) + m (2 π)}{m + m + m} = π$

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