The ratio of the moments of inertia of two uniform rings of radii $R$ and $nR$ about an axis passing through their centers and perpendicular to their planes is $1 : 8$. What is the value of $n$?

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 straight thin rod of mass $M$ and length $l$ about an axis perpendicular to its length and passing through its one end,is

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?

If $I_1$,$I_2$,and $I_3$ are the moments of inertia of a solid sphere,a hollow cylinder,and a ring,respectively,all having the same mass and radius,which of the following statements is correct?

If a spherical planet of mass $M$ and radius $R$ suddenly shrinks to half its size,and its mass reduces to half,what is the new moment of inertia of the planet about its diameter?