Two rods,each of mass $m$ and length $l$,are joined at their centers to form a cross. What is the moment of inertia of the cross about an axis passing through their common center and perpendicular to the plane of the rods?

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

$A$ flywheel rotates about its axis with a constant angular velocity. If a particle suddenly sticks to its rim,what will happen to its moment of inertia?

How does the moment of inertia depend on the angular momentum?

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.)

Consider two uniform discs of the same thickness and different radii $R_{1} = R$ and $R_{2} = \alpha R$ made of the same material. If the ratio of their moments of inertia $I_{1}$ and $I_{2}$,respectively,about their axes is $I_{1} : I_{2} = 1 : 16$,then the value of $\alpha$ is: