$A$ 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 $x/R$.

The equilateral triangle $ABC$ is cut from a thin solid sheet of wood. $D, E$ and $F$ are the midpoints of its sides as shown and $G$ is the centre of the triangle. The moment of inertia of the triangle about an axis passing through $G$ and perpendicular to the plane of the triangle is $I_0$. If the smaller triangle $DEF$ is removed from $ABC$,the moment of inertia of the remaining figure about the same axis is $I$. Then

$A$ circular plate of uniform thickness has a diameter of $56 \ cm$. $A$ circular part of diameter $42 \ cm$ is removed from one edge. What is the position of the centre of mass of the remaining part in $cm$?

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

The position vector of the centre of mass $\vec{r}_{cm}$ of an asymmetric uniform bar of negligible area of cross-section as shown in the figure is: