Moment of inertia of the rod about an axis passing through the centre and perpendicular to its length is $I_1$. The same rod is bent into a ring and its moment of inertia about the diameter is $I_2$. Then $I_1 / I_2$ is

$A$ wire of length $\ell$ and mass $M$ is bent into a semicircle of radius $r$ as shown in the figure. Calculate the moment of inertia about the axis $XX'$.

Two point masses of $0.3 \ kg$ and $0.7 \ kg$ are fixed at the ends of a rod of length $1.4 \ m$ and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum is located at a distance of

$A$ 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 circular wire of mass $M$ and radius $R$ about its diameter is .......

Four point masses each of mass $m$ are placed at the corners of a square $ABCD$ of side length $\ell$. What is the moment of inertia about an axis passing through $A$ and parallel to $BD$?