$A$ uniform square plate is shown in the figure. Four identical squares are removed from its corners. Where does the center of mass lie?

From a circular disc of radius $R$,a triangular portion is cut as shown in the figure. The distance of the center of mass $(COM)$ of the remaining disc from the center of the disc $O$ is:

The $x, y$ coordinates of the centre of mass of a uniform $L$-shaped lamina of mass $3\, kg$ are

$A$ spherical hollow is made in a lead sphere of radius $R,$ such that its surface touches the outside surface of the lead sphere and passes through the centre. What is the shift in the centre of mass of the lead sphere due to this?

$A$ semicircular portion of radius $r$ is cut from a uniform rectangular plate as shown in the figure. The distance of the centre of mass $C$ of the remaining plate from point $O$ is:

$A$ uniform square plate of side $a$ has a circular hole of diameter $a$ cut out from it as shown in the figure. The centre of the hole is at the centre of the square. The centre of mass of the remaining part is: