$A$ 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 ..............

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?

The rectangular plate shown in the figure is rotated in turn about $x-x'$,$y-y'$ and $z-z'$ axes passing through its centre of mass $O$. Its moment of inertia is

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

$A$ thin square plate of side $4R$ has a mass $M$. Four circles of radius $R$ are cut from it as shown. Calculate the moment of inertia of the remaining part about the $z$-axis passing through the center of the square.

In the triangular sheet shown,$PQ = QR = l$. If $M$ is the mass of the sheet,what is the moment of inertia about the axis $PR$?