There is a thin uniform disc of radius $\mathrm{R}$ and mass per unit area $\mathrm{\sigma }$, in which a hole of radius $\mathrm{R}/2$ has been cut out as shown in the figure. Inside the hole, a square plate of same mass per unit area $\mathrm{\sigma }$ is inserted so that its corners touch the periphery of the hole. The distance of the centre of mass of the system from the origin is

• Correct answer
  A

  $\frac{\text{R(}2-\mathrm{\pi })}{2\left(3\mathrm{\pi }+2\right)}$
• B

  $\frac{\text{R(}1-\mathrm{\pi })}{2\left(2\mathrm{\pi }+1\right)}$
• C

  $\frac{2\text{R}\pi }{2\left(3\pi +2\right)}$
• D

  $\frac{3\text{R}\pi }{2\left(2\pi +1\right)}$

Hence, the correct answer is option: 'A'.