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 . . . . . . .

The moment of inertia of a semicircular disc of mass $M$ and radius $R$ about the shown 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 ..........$m r^2$.

$A$ uniform square plate of side $a$ and mass $m$ is given. The moment of inertia of this plate about an axis perpendicular to the plate and passing through one of its corners is .......

$A$ thin metal wire of length $L$ and uniform linear mass density $Q$ is bent into a circular coil with $O$ as the center. The moment of inertia of the coil about the axis $XX'$ is:

The moment of inertia of a solid sphere,about an axis parallel to its diameter and at a distance of $x$ from it,is $I(x)$. Which one of the graphs represents the variation of $I(x)$ with $x$ correctly?