Three identical spheres,each of mass $M$ and radius $R$,are placed as shown in the figure. Consider an axis $XX'$ which passes through the diameter of the top sphere and is tangent to the two bottom spheres. The moment of inertia of the system consisting of these three spheres about the $XX'$ axis is:

Seven identical coins are rigidly arranged on a flat table in the pattern shown below,so that each coin touches its neighbours. Each coin is a thin disc of mass $m$ and radius $r$. Note that the moment of inertia of an individual coin about an axis passing through its centre and perpendicular to the plane of the coin is $\frac{m r^2}{2}$. The moment of inertia of the system of seven coins about an axis that passes through the point $P$ (the centre of the coin positioned directly to the right of the central coin) and perpendicular to the plane of the coins is ..........$m r^2$.

The moment of inertia of a rod of mass $40 \text{ kg}$ and length $3 \text{ m}$ about an axis $AB$ passing through its end and perpendicular to its length is equal to the moment of inertia of a solid sphere of mass $10 \text{ kg}$ and radius $R$ about an axis parallel to the $AB$ axis, with a separation of $3 \text{ m}$ between the axes, as shown in the figure. The value of $R$ is given as $\sqrt{\frac{\alpha}{2}}$. The value of $\alpha$ is . . . . . . .

Moment of inertia of a disc about an axis which is tangent and parallel to its plane is $I$. Then the moment of inertia of disc about a tangent,but perpendicular to its plane will be

What is the moment of inertia of a disc about one of its diameters?

The moment of inertia of a uniform square plate about an axis perpendicular to its plane and passing through the centre is $\frac{Ma^{2}}{6}$,where $M$ is the mass and $a$ is the side of the square plate. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is