There is a thin uniform disc of radius R and mass per unit area `sigma`, in which a hole of radius R/2 has been cut 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.

Options

A. `(R[2+pi])/(2[3pi+2])`
B. `(R[2-pi])/(2[3pi-2])`
C. `(R[2-pi])/(2[3pi+2])`
D. `(R[2-pi])/([3pi+2])`

Answer

C