Four thin rods of same mass $M$ and same length $l$ form a square as shown in the figure. The moment of inertia of this system about an axis passing through the centre $O$ and perpendicular to its plane is

The moment of inertia of a thin square plate $ABCD$ of uniform thickness about an axis passing through the centre $O$ and perpendicular to the plane of the plate is given by which of the following expressions? Here,$I_1, I_2, I_3,$ and $I_4$ are the moments of inertia about axes $1, 2, 3,$ and $4$ respectively,which lie in the plane of the plate as shown in the figure.

From a circular disc of radius $R$ and mass $9M$,a small disc of radius $\frac{R}{3}$ is removed concentrically. If the mass of the removed disc is $M$,what is the moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre?

$A$ solid cylinder has mass $M$,length $L$,and radius $R$. What is the moment of inertia of this cylinder about one of its generators?

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 $.........$

The moment of inertia of a circular disc of radius $2 \,m$ and mass $1 \,kg$ about an axis $XY$ passing through its center of mass and perpendicular to the plane of the disc is $2 \,kg \,m^2$. The moment of inertia about an axis parallel to the axis $XY$ and passing through the edge of the disc is