Four spheres,each of mass $M$ and diameter $2a$,are placed at the corners of a square of side $b$ as shown in the figure. Calculate the moment of inertia about the axis $BB'$.

From a uniform circular thin disc of mass $9 M$ and radius $R$,a small disc of radius $\frac{R}{3}$ is removed. The centre of the small disc is at a distance $\frac{2 R}{3}$ from the centre of the original disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through the centre of the original disc of radius $R$ is

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.)

$A$ circular plate of mass $M$ and radius $R$ has its density varying as $\rho(r) = \rho_0 r$,where $\rho_0$ is a constant and $r$ is the distance from its center. The moment of inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is $I = aMR^2$. The value of the coefficient $a$ is:

The moment of inertia of a solid cylinder about its own axis is equal to its moment of inertia about an axis passing through its center of gravity and perpendicular to its length. What is the relationship between its length $L$ and radius $R$?

Four spheres,each of mass $M$ and radius $r$,are situated at the four corners of a square of side $R$. The moment of inertia of the system about an axis perpendicular to the plane of the square and passing through its centre will be