Calculate the moment of inertia of a disc about an axis tangent to its inner circle and lying in the plane of the disc. The mass of the disc is $M$,the inner radius is $R_1$,and the outer radius is $R_2$.

The moment of inertia of a circular ring of mass $M$ and diameter $r$ about a tangential axis lying in the plane of the ring is

Three rods are arranged in the form of an equilateral triangle. Calculate the moment of inertia about an axis passing through the centroid and perpendicular to the plane of the triangle. (Each rod has mass $M$ and length $L$)

Four spheres of diameter $2a$ and mass $M$ are placed with their centres on the four corners of a square of side $b$. The moment of inertia of the system about an axis passing through one of the sides of the square is ..........

$A$ thin wire of length $l$ and uniform linear mass density $\rho$ is bent into a circular loop with centre $O$ and radius $r$ as shown in the figure. The moment of inertia of the loop about the axis $XX'$ 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).