The moment of inertia of a square loop made of four uniform solid cylinders,each having radius $R$ and length $L$ $(R < L)$,about an axis passing through the midpoints of opposite sides,is (Take the mass of the entire loop as $M$):

$I_1$ is the moment of inertia of a circular disc about an axis passing through its centre and perpendicular to the plane of the disc. $I_2$ is its moment of inertia about an axis $AB$ perpendicular to the plane and parallel to the axis $CM$ at a distance $\frac{2R}{3}$ from the centre. The ratio of $I_2$ to $I_1$ is $\frac{I_2}{I_1} = \frac{x}{9}$. The value of $x$ is ($R =$ radius of the disc).

Four thin metal rods,each of mass $M$ and length $L$,are welded end to end to form a square. The moment of inertia of the system about an axis passing through the centre of the square and perpendicular to its plane is

Seven identical discs each of mass $M$ and radius $R$ are arranged in a hexagonal plane pattern so as to touch each neighbour disc as shown in the figure. The moment of inertia of the system of seven discs about an axis passing through the centre of the central disc and normal to the plane of all discs is

The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through which of the following points?

Consider a thin metal strip of mass $1 \, kg$ and length $5 \, m$. Calculate its moment of inertia about an axis perpendicular to the strip and located at $100 \, cm$ on the strip from one of its ends. (Assume the breadth of the strip is negligible.)