Five masses,each of $2\, kg$,are placed on a horizontal circular disc that can rotate about a vertical axis passing through its center. All masses are equidistant from the axis at a distance of $10\, cm$. Calculate the moment of inertia of the whole system in $gm-cm^2$. (Assume the disc has negligible mass.)

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 ratio of the moments of inertia of two uniform rings of radii $R$ and $nR$ about an axis passing through their centers and perpendicular to their planes is $1 : 8$. What is the value of $n$?

The radius of gyration of a rod of length $L$ and mass $M$ about an axis perpendicular to its length and passing through a point at a distance $L/3$ from one of its ends,is :-

$A$ solid square plate is spun around different axes with the same angular speed. In which of the following choices of axis of rotation will the kinetic energy of the plate be the largest?

If the radius of gyration of a thin circular ring about an axis passing through its centre and perpendicular to its plane is $10 \sqrt{2} \,cm$, then its radius of gyration about its diameter is