$A$ thin metal wire of length $L$ and uniform linear mass density $Q$ is bent into a circular coil with $O$ as the center. The moment of inertia of the coil about the axis $XX'$ is:

Match the items in Column-$I$ with those in Column-$II$.

Column-$I$	Column-$II$
$(1)$ Moment of inertia of a solid sphere about its diameter	$(a)$ $\frac{2}{3}MR^2$
$(2)$ Moment of inertia of a solid sphere about a tangent	$(b)$ $\frac{2}{5}MR^2$
	$(c)$ $\frac{7}{5}MR^2$

The moment of inertia of a sphere (mass $M$ and radius $R$) about its diameter is $I$. Four such spheres are arranged as shown in the figure. The moment of inertia of the system about the axis $XX'$ will be (in $,I$)

$I_1$ is the moment of inertia of a circular disc about an axis passing through its centre and perpendicular to the plane of the disc. $I_2$ is its moment of inertia about an axis $AB$ perpendicular to the plane and parallel to the axis $CM$ at a distance $\frac{2R}{3}$ from the centre. The ratio of $I_2$ to $I_1$ is $\frac{I_2}{I_1} = \frac{x}{9}$. The value of $x$ is ($R =$ radius of the disc).

$A$ lamina is made by removing a small disc of diameter $2R$ from a bigger disc of uniform mass density and radius $2R$,as shown in the figure. The moment of inertia of this lamina about axes passing through $O$ and $P$ is $I_0$ and $I_P$,respectively. Both these axes are perpendicular to the plane of the lamina. The ratio $\frac{I_P}{I_0}$ to the nearest integer is:

$A$ solid sphere of radius $R$ and mass $M$ is rotating about its diameter. The moment of inertia of the solid sphere rotating about an axis at a distance $R/3$ from the centre and parallel to that diameter is