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

$A$ uniform square plate of side $a$ has a hole of side $b$ cut out of it as shown in the figure. The hole is centered at $(a/4, a/4)$ from the center of the square plate. The distance of the center of mass of the remaining part from the center of the square plate is:

$A$ 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.

The figure shows a composite system of two uniform rods of lengths as indicated. The coordinates of the centre of mass of the system of rods are ...........

$A$ square shaped hole of side $l = \frac{a}{2}$ is carved out at a distance $d = \frac{a}{2}$ from the centre $O$ of a uniform circular disk of radius $a$. If the distance of the centre of mass of the remaining portion from $O$ is $-\frac{a}{X}$,find the value of $X$ (to the nearest integer).

The figure shows a uniform square plate from which four identical small squares have been removed from the corners. If square $1$ is removed,where will the center of mass $(C.M.)$ be located?