If the radius of a solid sphere is $35\,cm,$ calculate the radius of gyration when the axis is along a tangent.

Two discs having moment of inertia $I_1$ and $I_2$ are made from the same material and have the same mass. Their thicknesses and radii are $t_1, t_2$ and $R_1, R_2$ respectively. The relation between the moment of inertia of each disc about an axis passing through its centre and perpendicular to its plane and its thickness is:

$A$ circular disc is made using iron and aluminum such that its moment of inertia about its geometric axis is maximum. For this to happen:

Find the moment of inertia of a ring about an axis passing through the centre and perpendicular to its plane.

If a spherical planet of mass $M$ and radius $R$ suddenly shrinks to half its size,and its mass reduces to half,what is the new moment of inertia of the planet about its diameter?

From a uniform wire,two circular loops are made: $(i)\ P$ of radius $r$ and $(ii)\ Q$ of radius $nr$. If the moment of inertia of $Q$ about an axis passing through its center and perpendicular to its plane is $8$ times that of $P$ about a similar axis,the value of $n$ is (diameter of the wire is very much smaller than $r$ or $nr$).