The wheels of moving vehicles are made hollow in the middle and thick at the rim because...

Three rods each of length $L$ and mass $M$ are placed along $X$,$Y$,and $Z$-axes in such a way that one end of each rod is at the origin. The moment of inertia of this system about the $Z$-axis is

Let $M$ and $L$ be the mass and length of a thin uniform rod,respectively. In the $1^{\text{st}}$ case,the axis of rotation passes through the center and is perpendicular to its length. In the $2^{\text{nd}}$ case,the axis of rotation passes through one end and is perpendicular to its length. The ratio of the radius of gyration in the first case to the second case is:

Three point masses $m_1, m_2, m_3$ are located at the vertices of an equilateral triangle of side length $a$. The moment of inertia of the system about an axis along the altitude of the triangle passing through $m_1$ 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?

The moments of inertia of a non-uniform circular disc (of mass $M$ and radius $R$) about four mutually perpendicular tangents $AB, BC, CD, DA$ are $I_1, I_2, I_3$ and $I_4$,respectively (the square $ABCD$ circumscribes the circle). The distance of the centre of mass of the disc from its geometrical centre is given by