Two discs of same mass and same thickness have densities as $17 \, g/cm^3$ and $51 \, g/cm^3$. The ratio of their moment of inertia about their central axes is .........

$A$ solid hemisphere and a hemispherical shell are joined as shown. Both of them have a mass of $m/2$ individually. Find the moment of inertia about the axis $AB$.

What is the $SI$ unit of the radius of gyration?

The moment of inertia of a thin uniform rod about a perpendicular axis passing through one of its ends is $I$. Now,the rod is bent into a ring and its moment of inertia about its diameter is $I_{1}$. Then $\frac{I}{I_{1}}$ is:

Two point masses of $0.3 \ kg$ and $0.7 \ kg$ are fixed at the ends of a rod of length $1.4 \ m$ and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum is located at a distance of

The moment of inertia of a sphere of mass $M$ and radius $R$ is $I.$ If $M$ is kept constant and a graph is plotted between $I$ and $R,$ then its form would be: