Two rods of equal length $(l)$ and equal mass $M$ are kept along the $x$ and $y$ axes respectively,such that their center of mass lies at the origin. The moment of inertia about the line $y = x$ is ...........

The moment of inertia of a solid disc rotating about its diameter is $2.5$ times higher than the moment of inertia of a ring rotating in a similar way. The moment of inertia of a solid sphere which has the same radius as the disc and is rotating in a similar way,is $n$ times higher than the moment of inertia of the given ring. Here,$n=$ . . . . . . . Consider all the bodies have equal masses.

If a solid sphere and a solid cylinder of the same radius and density rotate about their own axes,which one will have a greater moment of inertia? (Assume $L = R$)

The ratio of masses and radii of two circular rings are $1 : 2$ and $2 : 1$ respectively. What is the ratio of their moments of inertia about their central axes?

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

Two rings have their moments of inertia in the ratio $4 : 1$ and their diameters are in the ratio $4 : 1$. The ratio of their masses is