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

$A$ circular disc of radius $b$ has a hole of radius $a$ at its centre (see figure). If the mass per unit area of the disc varies as $\sigma(r) = \frac{\sigma_0}{r}$,then the radius of gyration of the disc about its axis passing through the centre is

The moment of inertia $I$ of a solid sphere having fixed volume depends upon its volume $V$ as

Two rings made of the same material and having the same thickness have radii of $0.2 \ m$ and $0.6 \ m$. The ratio of their moments of inertia is:

$A$ straight rod of length $L$ is made of a material having mass per unit length $m(x) = \lambda|x|$, where $x$ is measured from the center of the rod. The moment of inertia about an axis perpendicular to the rod and passing through one end of the rod is to be calculated. Given $L = 1 \ m$ and $\lambda = 16 \ kg/m^2$.

$A$ thin wire of length $l$ and mass $M$ is bent in the form of a semi-circle. What is its moment of inertia about an axis passing through the ends of the wire?