Find the moment of inertia of a ring about an axis passing through the centre and perpendicular to its plane.

$A$ circular disc is to be made by using iron and aluminium,so that it acquires maximum moment of inertia about its geometrical axis. This is possible with:

Three particles,each of mass $m$,are placed at the vertices of an equilateral triangle $ABC$ of side length $l$. What is the moment of inertia of the system about the axis $AX$ in the plane of $ABC$,as shown in the figure?

Radius of gyration of a body depends on

$A$ circular disc $X$ of radius $R$ is made from an iron plate of thickness $t$,and another disc $Y$ of radius $4R$ is made from an iron plate of thickness $\frac{t}{4}$. The ratio of the moment of inertia $\frac{I_Y}{I_X}$ is:

Why does a solid sphere have a smaller moment of inertia than a hollow cylinder of the same mass and radius,about an axis passing through their axes of symmetry?