Two uniform circular discs having the same mass and the same thickness but different radii are made from different materials. The disc with the smaller rotational inertia is

What is the radius of gyration of a circular disc of radius $R$ about an axis passing through its center and perpendicular to its plane?

$A$ thin metal rod of mass $M$ and length $L$ is cut into four equal parts by cutting it perpendicular to its length. If the moment of inertia of the rod about an axis passing through its centre and perpendicular to its length is $I$,then the moment of inertia of each part about an axis passing through its own centre and perpendicular to its length is:

Two spheres $A$ and $B$,each of mass $5 \ kg$,are attached to the ends of a light rod of length $1 \ m$. Treating the spheres as point masses,find the ratio of the moment of inertia of the system about an axis passing through $A$ to that about an axis passing through the center of the rod,both axes being perpendicular to the rod.

$A$ 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

Two point masses of $0.3 \ kg$ and $0.7 \ kg$ are fixed at the ends of a rod of length $1.4 \ m$ and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum is located at a distance of