The moment of inertia of a regular circular disc of mass $0.4\, kg$ and radius $100\, cm$ about an axis perpendicular to the plane of the disc and passing through its centre is ...... $kg\, m^2$.

$A$ thin uniform rectangular plate of mass $2 \, kg$ is placed in the $xy$-plane as shown in the figure. The moment of inertia about the $x$-axis is $I_{x}=0.2 \, kg \cdot m^{2}$ and the moment of inertia about the $y$-axis is $I_{y}=0.3 \, kg \cdot m^{2}$. The radius of gyration of the plate about the axis passing through $O$ and perpendicular to the plane of the plate is (in $ \, cm$)

Four solid spheres,each of mass $M$ and radius $R$,are placed at the four corners of a square of side length $a$. Find the moment of inertia of the system about an axis coinciding with one of the sides of the square.

For the same total mass,which of the following will have the largest moment of inertia about an axis passing through its centre of mass and perpendicular to the plane of the body?

$A$ disc of radius $R$ and thickness $\frac{R}{6}$ has moment of inertia $I$ about an axis passing through its centre and perpendicular to its plane. The disc is melted and recast into a solid sphere. The moment of inertia of the sphere about its diameter is

$A$ solid sphere of mass $M$ and radius $R$ is divided into two unequal parts. The first part has a mass of $\frac{7M}{8}$ and is converted into a uniform disc of radius $2R$. The second part is converted into a uniform solid sphere. Let $I_1$ be the moment of inertia of the disc about its axis and $I_2$ be the moment of inertia of the new sphere about its axis. The ratio of $I_1/I_2$ is given by