Four rods,each of mass $M$ and length $l$,are arranged to form a square as shown in the figure. What is the moment of inertia of this square about an axis passing through $O$ and perpendicular to the plane of the square?

The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through which of the following points?

$A$ square plate of mass $m$ and side $a$ has a moment of inertia about an axis perpendicular to its plane and passing through one of its corners equal to $\alpha \,ma^2$. Then $\alpha$ is:

Two spheres each of mass $M$ and radius $R$ are connected with a massless rod of length $4R$. The moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod will be

The moment of inertia of a square frame about an axis passing through its center of mass and perpendicular to its plane is $20 \ kg \cdot m^2$. The moment of inertia about an axis touching its side and lying in the plane of the frame is ........ $kg \cdot m^2$.

From a uniform circular thin disc of mass $9 M$ and radius $R$,a small disc of radius $\frac{R}{3}$ is removed. The centre of the small disc is at a distance $\frac{2 R}{3}$ from the centre of the original disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through the centre of the original disc of radius $R$ is