If a spherical planet of mass $M$ and radius $R$ suddenly shrinks to half its size,and its mass reduces to half,what is the new moment of inertia of the planet about its diameter?

Three point masses,each of mass $m$,are placed at the corners of an equilateral triangle of side $L$. The moment of inertia of the system about an axis passing through one of the vertices and parallel to the side joining the other two vertices will be

Two rings of the same material have radii $R$ and $nR$ respectively. The ratio of their moments of inertia about an axis passing through their centers and perpendicular to their planes is $1 : 8$. The value of $n$ is:

Why does a solid sphere have a smaller moment of inertia than a hollow cylinder of the same mass and radius,about an axis passing through their axes of symmetry?

$A$ solid sphere $A$ is rotating about an axis $PQ$. If the radius of the sphere is $5 \, cm$ and the distance of its center from the axis $PQ$ is $10 \, cm$,then its radius of gyration about $PQ$ will be $\sqrt{x} \, cm$. The value of $x$ is $................$.

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: