Two rings of radius $R$ and $nR$ having different masses and made up of the same wire have the ratio of moment of inertia about an axis passing through the centre as $1 : 8$. The value of $n$ is

The moment of inertia of a circular wire of mass $M$ and radius $R$ about its diameter is .......

Consider a sphere of mass $M$ and radius $R$ centered at the origin. The density of the material of the sphere is $\rho = A r^\alpha$, where $r$ is the radial distance, and $\alpha$ and $A$ are constants. If the moment of inertia of the sphere about the axis passing through the centre is $\frac{6}{7} M R^2$, then the value of $\alpha$ is

Two rings of radius $R$ and $nR$ made of the same material have a ratio of moment of inertia about an axis passing through their centers and perpendicular to their planes as $1:8$. The value of $n$ is (mass per unit length $= \lambda$).

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

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 $L = R$)