Four spheres,each of mass $M$ and radius $a$,are placed at the four corners of a square of side $b$. Calculate the moment of inertia of the system about one of the sides of the square as the axis.

Consider a uniform horizontal solid cylinder of mass $10 \,kg$ such that its length is $9$ times its radius. Let the radius be $40 \,cm$. Calculate the moment of inertia of the cylinder about a line passing through its edge and perpendicular to its axis.

If the moment of inertia of a thin circular ring about an axis passing through its edge and perpendicular to its plane is $I$,then the moment of inertia of the ring about its diameter is

$A$ square plate of mass $m$ and side $a$ has a moment of inertia about an axis perpendicular to its plane and passing through one of its corners equal to $\alpha \,ma^2$. Then $\alpha$ is:

$A$ lamina is made by removing a small disc of diameter $2R$ from a bigger disc of uniform mass density and radius $2R$,as shown in the figure. The moment of inertia of this lamina about axes passing through $O$ and $P$ is $I_0$ and $I_P$,respectively. Both these axes are perpendicular to the plane of the lamina. The ratio $\frac{I_P}{I_0}$ to the nearest integer is:

For the given uniform square lamina $ABCD$,whose centre is $O$,which of the following relations is correct?