Two discs of same mass and same thickness have densities as $17 \, g/cm^3$ and $51 \, g/cm^3$. The ratio of their moment of inertia about their central axes is .........

$A$ uniform square plate $S$ (side $c$) and a uniform rectangular plate $R$ (sides $b, a$) have identical areas and masses. Show that:
$(i) \frac{I_{xR}}{I_{xS}} < 1$
$(ii) \frac{I_{yR}}{I_{yS}} > 1$
$(iii) \frac{I_{zR}}{I_{zS}} > 1$

Two discs of the same thickness but different radii are made of two different materials such that their masses are equal. The densities of the materials are in the ratio $1:3$. The ratio of the moments of inertia of the discs about the axes passing through their centers and perpendicular to their planes is:

$A$ thin metal wire of length $L$ and mass $M$ is bent to form a semicircular ring as shown. The moment of inertia about the axis $XX^1$ passing through its ends is:

The radius of gyration of a uniform rod of length $l$ about an axis passing through one of its ends and perpendicular to its length is

Find the moment of inertia of the system of particles about the axis $OA$ passing through point $O$.