Two semicircular rings of linear mass densities λ and 2λ 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 −2Rπ,0 and 2Rπ,0.∴ x-coordinates of centre of mass of complete ring ism−2Rπ+2m2Rπ3m=2R3π