There is a thin uniform disc of radius \( \mathrm{R} \) and mass per P unit area \( \sigma \), i...

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There is a thin uniform disc of radius \( \mathrm{R} \) and mass per
P unit area \( \sigma \), in which a hole of radius \( \mathrm{R} / 2 \) has been cut

W out as shown in the figure. Inside the hole a square plate of same mass per unit area \( \sigma \) is inserted so that its corners touch the periphery of the hole. Find centre of mass of the system.
(1) \( \frac{R[2+\pi]}{2[3 \pi+2} \)
(2) \( \frac{R[2-\pi]}{2[3 \pi-2} \)
(3) \( \frac{R[2-\pi]}{2[3 \pi+2} \)
(4) \( \frac{R[2-\pi]}{[3 \pi+2} \)
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