$A$ spherical shell has a mass one-fourth that of a solid sphere,and both have the same moment of inertia $(M.I.)$ about their respective diameters. The ratio of their radii will be:

The densities of two solid spheres $A$ and $B$ of the same radii $R$ vary with radial distance $r$ as $\rho_A(r) = k \left(\frac{r}{R}\right)$ and $\rho_B(r) = k \left(\frac{r}{R}\right)^5$,respectively,where $k$ is a constant. The moments of inertia of the individual spheres about axes passing through their centres are $I_A$ and $I_B$,respectively. If $\frac{I_B}{I_A} = \frac{n}{10}$,the value of $n$ is

The moment of inertia of a thin uniform rod about a perpendicular axis passing through one of its ends is $I$. Now,the rod is bent into a ring and its moment of inertia about its diameter is $I_{1}$. Then $\frac{I}{I_{1}}$ is:

$A$ circular disc is made using iron and aluminum. To maximize the moment of inertia about its geometric axis,which configuration is preferred?

Four masses are fixed on a massless rod as shown in the figure. The moment of inertia about the axis $P$ is about ....... $kg \cdot m^2$.

The radius of gyration of a uniform thin rod of length $L$ about an axis passing normally through its centre of mass is: