The sector of a circular plate shown in the figure has its center of mass at $y_{CM} =$

$A$ thin uniform circular disc has mass $9M$ and radius $R$. $A$ small circular part of radius $R/3$ is cut from the disc as shown in the figure. Calculate the moment of inertia of the remaining part about an axis passing through the center $O$ and perpendicular to the plane of the disc.

$A$ circular disc of radius $R$ is removed from one end of a bigger circular disc of radius $2R$. The centre of mass of the new disc is at a distance $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is

$A$ uniform square plate of side $a$ has a circular hole of diameter $a/2$ cut out from it as shown in the figure. The center of the hole is at $a/4$ from the center of the square plate. The distance of the center of mass of the resulting plate from the center of the square is:

$A$ circular plate of uniform thickness with a diameter of $56\, cm$ has its center at the origin. $A$ circular part with a diameter of $42\, cm$ is removed from one edge. What is the distance of the center of mass of the remaining part in $cm$?

The coordinates of the centre of mass of a uniform $L$-shaped plate of mass $3 \ kg$ shown in the figure is: