The ratio of the radii of two solid spheres of same mass is $2:3$. The ratio of the moments of inertia of the spheres about their diameters 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

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

$A$ wheel of mass $10 \ kg$ has a moment of inertia of $160 \ kg \cdot m^2$ about its own axis. The radius of gyration is ........ $m.$

Two rings of same mass $m$ and radius $R$ are placed with their planes perpendicular to each other and centres at a common point. The radius of gyration of the system about an axis passing through the centre and perpendicular to the plane of one ring is ............

What is the moment of inertia of a cylinder of diameter $D$ and length $L$ about an axis passing through its center of gravity and perpendicular to its length?