Four particles each of mass $M$ are placed at the corners of a square of side $L$. The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is

What is the moment of inertia of a solid sphere of radius $R$ and density $\rho$ about its diameter?

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?

What is the moment of inertia of a thin circular disc about its diameter? ($M$ is the mass and $R$ is the radius of the disc.)

$A$ 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 ........ $m.$

Let $l$ be the moment of inertia of a uniform square plate about an axis $AB$ that passes through its centre and is parallel to two of its sides. $CD$ is a line in the plane of the plate that passes through the centre of the plate and makes an angle $\theta$ with $AB$. The moment of inertia of the plate about the axis $CD$ is then equal to: