For the adjoining diagram,the incorrect relation between $I_{1}, I_{2}$ and $I_{3}$ is ($I$ = moment of inertia).

Three rods each of length $L$ and mass $M$ are placed along $X$,$Y$,and $Z$-axes in such a way that one end of each rod is at the origin. The moment of inertia of this system about the $Z$-axis is

The radius of gyration of a uniform thin rod of length $L$ about an axis passing normally through its centre of mass is:

The figure shows an isosceles triangular plate of mass $M$ and base $L$. The angle at the apex is $90^o$. The apex lies at the origin and the base is parallel to the $X$-axis. The moment of inertia of the plate about the $z$-axis is

$A$ thin rod of length $L$ and mass $M$ is bent at the middle point $O$ at an angle of $60^{\circ}$ as shown in the figure. The moment of inertia of the rod about an axis passing through $O$ and perpendicular to the plane of the rod will be:

$A$ ring and a solid sphere rotating about an axis passing through their centers have same radii of gyration. The axis of rotation is perpendicular to the plane of the ring. The ratio of the radius of the ring to that of the sphere is $\sqrt{\frac{2}{x}}$. The value of $x$ is $.......$