The radius of gyration of a uniform rod of length $l$ about an axis passing through a point $\frac{l}{4}$ away from the centre of the rod and perpendicular to it is:

$A$ thin uniform rod of length $L$ and mass $M$ is bent at the middle point $O$ at an angle of $45^{\circ}$ as shown in the figure. The moment of inertia of the system about an axis passing through $O$ and perpendicular to the plane of the bent rod is:

Calculate the moment of inertia of the system shown in the figure about the axis of rotation $XX'$.

The moment of inertia of a uniform thin rod of mass $m$ and length $\ell$ about a perpendicular axis passing through one end is $I_{1}$. The same rod is bent into a ring and its moment of inertia about a diameter is $I_{2}$. If $\frac{I_{1}}{I_{2}} = \frac{x \pi^{2}}{3}$,then the value of $x$ will be ...............

One circular ring and one circular disc,both having the same mass and radius. The ratio of their moments of inertia about the axis passing through their centers and perpendicular to their planes will be:

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