Three rods of the same mass are placed as shown in figure. What will be the coordinates of centre of mass of the system?

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$[\sqrt{2} a, \sqrt{2} a,]$

$[\frac{a}{2}, \frac{a}{2}]$

$[\frac{a}{3}, \frac{a}{3}]$

$[\frac{a}{\sqrt{2}}, \frac{a}{\sqrt{2}}]$

answer is D.

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Detailed Solution

As shown in figure, centre of mass of respective rods are at their respective mid-points.

Hence centre of mass of the system has coordinates $(X_{C M}, Y_{C M})$ , then

$X_{C M} = \frac{m \times \frac{a}{2} + m \times \frac{a}{2} + m \times 0}{3 m} = \frac{a}{3}$

$Y_{C M} = \frac{m \times 0 + m \times \frac{a}{2} + m \times \frac{a}{2}}{3 m} = \frac{a}{3}$

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