Two semicircular rings of linear mass densities $\lambda$ and 2$\lambda$ and of radius 'R' each are joined to form a complete ring. The distance of the center of the mass of complete ring from its center is

Let the two half rings be placed in left and right of y-axis with centre as shown in figure.
Then the coordinate of centre of mass of left and right half rings are $\left(-\frac{2R}{\pi },0\right)$ and $\left(\frac{2R}{\pi },0\right)$.

$\therefore$ x-coordinates of centre of mass of complete ring is

$\frac{m\left(-\frac{2R}{\pi }\right)+2m\left(\frac{2R}{\pi }\right)}{3m}=\frac{2R}{3\pi }$