The moment of inertia of a big drop is $I$. If $8$ droplets are formed from the big drop,then the moment of inertia of a small droplet 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

Three thin rods,each of length $L$ and mass $M$,are placed along the $x, y,$ and $z-$ axes such that one end of each rod is at the origin. The moment of inertia of this system about the $z-$ axis is:

$A$ thin rod of total length $4l$ and total mass $4M$ is bent into the shape shown in the figure. Each segment has length $l$ and mass $M$. What is the moment of inertia of the rod about the axis passing through point $O$ and perpendicular to the plane of the paper?

The figure shows the variation of the moment of inertia of a uniform rod about an axis passing through its centre and inclined at an angle $\theta$ to the length of the rod. The moment of inertia of the rod about an axis passing through one of its ends and making an angle $\theta = \frac{\pi}{3}$ with the rod will be ........ $kg-m^2$.

The moment of inertia of a uniform rod of length $2l$ and mass $m$ about an axis $xx'$ passing through its centre and inclined at an angle $\alpha$ is