Four masses are attached to a light circular frame of radius $a$ as shown in the figure. The radius of gyration of this system about an axis passing through the center $O$ of the circular frame and perpendicular to its plane is:

The moment of inertia of a thin circular lamina of mass $1\,kg$ and diameter $0.2\,m$ rotating about one of its diameters is

An annular ring has mass $10 \ kg$ and inner and outer radii are $5 \ m$ and $10 \ m$ respectively. Its moment of inertia about an axis passing through its centre and perpendicular to its plane is

$A$ disc of radius $R$ and thickness $\frac{R}{6}$ has moment of inertia $I$ about an axis passing through its centre and perpendicular to its plane. The disc is melted and recast into a solid sphere. The moment of inertia of the sphere about its diameter is

$A$ quarter circular sector is cut from a uniform circular disc. The mass of this sector is $M$. It is rotated about an axis passing through the center of the original disc and perpendicular to its plane. The moment of inertia of this sector about the axis of rotation is:

The figure shows a uniform rod of length $L$ and mass $M$ lying along the $x$-axis with one end at the origin $O$. The locus of all points $(x, y)$ in the $xy$-plane,about which the moment of inertia of the rod is the same as that about $O$,is: