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

Two discs of same mass and different radii are made of different materials such that their thicknesses are $1\,cm$ and $0.5\,cm$ respectively. The densities of materials are in the ratio $3:5$. The moment of inertia of these discs respectively about their diameters will be in the ratio of $\frac{x}{6}$. The value of $x$ is $.......$.

Two discs of same mass and same thickness $(t)$ are made from two different materials of densities $d_1$ and $d_2$ respectively. The ratio of the moment of inertia $I_1$ to $I_2$ of the two discs about an axis passing through the centre and perpendicular to the plane of the disc is:

The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is

The ratio of the radius of gyration of a ring to that of a disc (both circular) of the same radius and mass,about a tangential axis perpendicular to the plane is

We have two spheres,one solid and one hollow. Their moments of inertia about their respective diameters are equal. The ratio of their radii will be: