Two rods of equal mass $m$ and length $l$ lie along the $x$-axis and $y$-axis with their centers at the origin. What is the moment of inertia of both about the line $x=y$?

$A$ straight rod of length $L$ is made of a material having mass per unit length $m(x) = \lambda|x|$, where $x$ is measured from the center of the rod. The moment of inertia about an axis perpendicular to the rod and passing through one end of the rod is to be calculated. Given $L = 1 \ m$ and $\lambda = 16 \ kg/m^2$.

The moment of inertia of a sphere of mass $M$ and radius $R$ about an axis passing through its centre is $\frac{2}{5} M R^2$. The radius of gyration of the sphere about a parallel axis to the above and tangent to the sphere is

The radius of gyration of a solid sphere of radius $R$ and mass $M$ about its diameter is $K_d$ and that about a tangent of a solid sphere is $K_t$. The ratio of $K_d$ to $K_t$ is

The moment of inertia of a solid cylinder of mass $2.5 \ kg$ and radius $10 \ cm$ about its axis is (in $kg \ m^2$)

Two uniform circular discs having the same mass and the same thickness but different radii are made from different materials. The disc with the smaller rotational inertia is