$A$ disk of radius $R$ is removed from a larger disk of radius $2R$. The circumferences of both disks are tangent to each other. The center of mass of the new disk is at a distance $x$ from the center of the larger disk. Find the value of $x/R$.

$A$ circular hole of radius $3 \text{ cm}$ is cut out from a uniform circular disc of radius $6 \text{ cm}$. The centre of the hole is at $3 \text{ cm}$ from the centre of the original disc. The distance of the centre of gravity of the resulting flat body from the centre of the original disc is: (in $\text{ cm}$)

The position of the centre of mass of the uniform plate as shown in the figure is

Consider a circular disc of radius $20 \ cm$ with centre located at the origin. $A$ circular hole of radius $5 \ cm$ is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of the centre of mass of the residual or remaining disc from the origin will be (in $cm$)

$A$ circular portion of radius $R_2$ has been removed from one edge of a circular disc of radius $R_1$. The correct expression for the centre of mass for the remaining portion of the disc is

In the figure shown,a hole of radius $2 \, cm$ is made in a semicircular disc of radius $6 \, cm$ at a distance $8 \, cm$ from the centre $C$ of the disc. The distance of the centre of mass of this system from point $C$ is ......... $cm$.