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:

$A$ thin wire of length $l$ having linear mass density $\rho$ is bent into a circular loop with $C$ as its centre,as shown in the figure. The moment of inertia of the loop about the line $AB$ 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

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 . . . . . . .

From a circular disc of radius $R$ and mass $9M$,a small disc of radius $\frac{R}{3}$ is removed. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through $O$ is:

$A$ thin square plate $ABCD$ has a uniform thickness. What is the moment of inertia about an axis passing through its center and perpendicular to its plane?