$A$ solid sphere of mass $500\,g$ and radius $5\,cm$ is rotated about one of its diameters with an angular speed of $10\,rad\,s^{-1}$. If the moment of inertia of the sphere about its tangent is $x \times 10^{-2}$ times its angular momentum about the diameter,then the value of $x$ will be ..............

$A$ thin wire of length $L$ and uniform linear mass density $\rho$ is bent into a circular loop with centre at $O$ as shown. The moment of inertia of the loop about the axis $XX'$ is

According to the parallel axis theorem,$I = I_C + Mx^2$. Which of the following graphs of $I$ versus $x$ is correct?

Three rings each of mass $M$ and radius $R$ are arranged as shown in the figure. The moment of inertia of the system about the axis $YY'$ is:

$A$ small circular disc of radius $R/3$ is cut from a larger circular disc of radius $R$ and mass $9M$. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through $O$ is:

$A$ 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: