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(C) Let the three rods be $R_1$,$R_2$,and $R_3$ with mass $m$ each.$1$. Rod $R_1$ lies on the $x$-axis from $(0,0)$ to $(2a,0)$. Its centre of mass is

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$\left(\frac{2a}{3}, \frac{a}{3}\right)$

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(C) Let the three rods be $R_1$,$R_2$,and $R_3$ with mass $m$ each.$1$. Rod $R_1$ lies on the $x$-axis from $(0,0)$ to $(2a,0)$. Its centre of mass is at $(x_1, y_1) = (a, 0)$.$2$. Rod $R_2$ lies on the $y$-axis from $(0,0)$ to $(0,a)$. Its centre of mass is at $(x_2, y_2) = (0, a/2)$.$3$. Rod $R_3$ connects $(2a,0)$ and $(0,a)$. Its centre of mass is at $(x_3, y_3) = (a, a/2)$.The coordinates of the centre of mass $(X_{cm}, Y_{cm})$ are given by:$X_{cm} = \frac{m(x_1 + x_2 + x_3)}{3m} = \frac{a + 0 + a}{3} = \frac{2a}{3}$$Y_{cm} = \frac{m(y_1 + y_2 + y_3)}{3m} = \frac{0 + a/2 + a/2}{3} = \frac{a}{3}$Thus,the centre of mass is at $\left(\frac{2a}{3}, \frac{a}{3}\right)$.

Three rods of the same mass are placed as shown in the figure. The coordinates of the centre of mass of the system are:

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