$A$ spherical cavity of radius $r$ is carved out of a uniform solid sphere of radius $R$ as shown in the figure below. The distance of the centre of mass of the resulting body from that of the solid sphere is given by

$A$ circular plate $A$ of radius $1.5 r$ is removed from one edge of a uniform circular plate $B$ of radius $2 r$. The distance of the centre of mass of the remaining portion from the centre of the plate $B$ is

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

$A$ smaller cube with side $b$ (depicted by dashed lines) is excised from a bigger uniform cube with side $a$ as shown below,such that both cubes have a common vertex $P$. Let $X = a/b$. If the centre of mass of the remaining solid is at the vertex $O$ of the smaller cube,then $X$ satisfies:

$A$ carpenter has constructed a toy as shown in the adjoining figure. If the density of the material of the sphere is $12$ times that of the cone,the position of the centre of mass of the toy is given by

In the figure shown,find the distance of the centre of mass of a system of a uniform circular plate of radius $3R$ from $O$,in which a hole of radius $R$ is cut whose centre is at a distance of $2R$ from the centre of the large circular plate.