The moment of inertia of a rod of mass $M$ and length $L$ about an axis passing through a point midway between the center and the end is:

$A$ solid sphere of mass $5 \ kg$ and radius $10 \ cm$ is kept in contact with another solid sphere of mass $10 \ kg$ and radius $20 \ cm$. The moment of inertia of this pair of spheres about the tangent passing through the point of contact is . . . . . . $kg \cdot m^{2}$.

Three thin metal rods,each of mass $M$ and length $L$,are welded to form an equilateral triangle. The moment of inertia of the composite structure about an axis passing through the centre of mass of the structure and perpendicular to its plane is

From a disc of mass $M$ and radius $R$,a circular hole of diameter $R$ is cut whose rim passes through the centre. The moment of inertia of the remaining part of the disc about a perpendicular axis passing through the centre is

The moment of inertia of a circular disc of radius $2 \,m$ and mass $1 \,kg$ about an axis passing through the centre of mass but perpendicular to the plane of the disc is $2 \,kg \,m^{2}$. Its moment of inertia about an axis parallel to this axis but passing through the edge of the disc is (see the given figure).

The radius of gyration $K$ of a hollow sphere of mass $M$ and radius $R$ about an axis $XY$ is equal to $R$. The distance of that axis from the center of the sphere is $h$. The value of $h$ is