Two discs $A$ and $B$ each of radius $r$ and mass $m$ are attached as shown to form a system. The moment of inertia of this system about an axis perpendicular to the plane of the discs and passing through the center of disc $A$ is

What is the moment of inertia of a ring of mass $M$ and radius $R$ about a tangent to the circle of the ring in its own plane?

For the given uniform square lamina $ABCD$,whose centre is $O$,

The moment of inertia of a rod of mass $40 \text{ kg}$ and length $3 \text{ m}$ about an axis $AB$ passing through its end and perpendicular to its length is equal to the moment of inertia of a solid sphere of mass $10 \text{ kg}$ and radius $R$ about an axis parallel to the $AB$ axis, with a separation of $3 \text{ m}$ between the axes, as shown in the figure. The value of $R$ is given as $\sqrt{\frac{\alpha}{2}}$. The value of $\alpha$ is . . . . . . .

Let $I_1, I_2$ and $I_3$ be the moment of inertia of a uniform square plate of mass $M$ and side length $L$ about axes $AOC, xDx'$ and $yBy'$ respectively as shown in the figure. The ratio of the moments of inertia $I_1 : I_2 : I_3$ is:

$A$ thin wire of length $L$ and linear mass density $m$ is bent into a circular ring (in $x-y$ plane) with centre $C$ as shown in the figure. The moment of inertia of the ring about an axis $yy'$ will be: