Two rings have their moments of inertia in the ratio $2:1$ and their diameters are in the ratio $2:1$. The ratio of their masses is

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

Four particles each of mass $m$ are placed at the corners of a square of side length $l.$ The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is

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

If the length of a thin uniform rod is $L$ and the radius of gyration of the rod about an axis perpendicular to its length and passing through one end is $K$, then $K: L=$

Of the two eggs which have identical sizes,shapes and weights,one is raw and the other is half-boiled. The ratio between the moment of inertia of the raw egg to the half-boiled egg about their central axis is: