An iron circular disc $X$ has radius $R$ and thickness $t$. Another iron circular disc $Y$ has radius $4R$ and thickness $t/4$. The relationship between the moments of inertia $I_X$ and $I_Y$ of these two discs is .......

$A$ square sheet of edge length $L$ and uniform mass per unit area $\sigma$ is used to form a hollow cylinder. The moment of inertia of this cylinder about its central axis is

Two discs of same mass and different radii are made of different materials such that their thicknesses are $1\,cm$ and $0.5\,cm$ respectively. The densities of materials are in the ratio $3:5$. The moment of inertia of these discs respectively about their diameters will be in the ratio of $\frac{x}{6}$. The value of $x$ is $.......$.

$A$ thin wire of length $l$ and mass $M$ is bent in the form of a semi-circle. What is its moment of inertia about an axis passing through the ends of the wire?

The moment of inertia of a sphere of mass $M$ and radius $R$ about an axis passing through its centre is $\frac{2}{5} M R^2$. The radius of gyration of the sphere about a parallel axis to the above and tangent to the sphere is

Explain the radius of gyration.