If a solid sphere of mass $5 \, kg$ and a disc of mass $4 \, kg$ have the same radius $R$,then the ratio of the moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent is $\frac{x}{7}$. The value of $x$ is $.........$

$I_1$ 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).

Three rings each of mass $M$ and radius $R$ are arranged as shown in the figure. The moment of inertia of the system about the axis $YY'$ will be

The rectangular block shown in the figure is rotated about the $x-x$,$y-y$,and $z-z$ axes passing through its center of mass $O$. Its moment of inertia is:

The moment of inertia of a rod about an axis passing through its center of mass and perpendicular to it is $\frac{1}{12}ML^2$. If the rod is bent at the middle such that the two halves make an angle of $90^{\circ}$ in the same plane,what will be the moment of inertia of the system about the same axis?

$A$ thin wire of length $L$ and uniform linear mass density $\lambda$ is bent into a circular coil. The moment of inertia of this coil about a tangential axis in the plane of the coil is: