$A$ wire of mass $m$ and length $l$ is bent in the form of a circular ring. The moment of inertia of the ring about its axis is:

Three particles,each of mass $m \; g$,are situated at the vertices of an equilateral triangle $ABC$ of side $l \; cm$ (as shown in the figure). The moment of inertia of the system about a line $AX$ perpendicular to $AB$ and in the plane of $ABC$ in $g \cdot cm^2$ units will be:

The radius of gyration of a uniform rod of length $l$ about an axis passing through one of its ends and perpendicular to its length is

Three particles are connected by massless rods lying along the $y-$ axis. If the system rotates about the $x-$ axis with an angular speed of $2 \, rad/s$,the moment of inertia $(M.I.)$ of the system is ......... $kg \cdot m^2$.

Three thin uniform rods each of mass $M$ and length $L$ are placed along the three axes of a Cartesian coordinate system with one end of all the rods at the origin. The moment of inertia of the system of the rods about the $z$-axis is:

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