$A$ disc of radius $R$ and thickness $\frac{R}{6}$ has moment of inertia $I$ about an axis passing through its centre and perpendicular to its plane. The disc is melted and recast into a solid sphere. The moment of inertia of the sphere about its diameter is

$A$ cylinder of mass $500 \ g$ and radius $10 \ cm$ has a moment of inertia about an axis passing through its centre and parallel to its length equal to:

$A$ metallic solid sphere is rotating about its diameter as an axis of rotation. If the temperature is increased by $200^{\circ} C$, the percentage increase in its moment of inertia is (Coefficient of linear expansion of the metal $= 10^{-5} /^{\circ} C$) (in $\%$)

Five masses,each of $2\, kg$,are placed on a horizontal circular disc that can rotate about a vertical axis passing through its center. All masses are equidistant from the axis at a distance of $10\, cm$. Calculate the moment of inertia of the whole system in $gm-cm^2$. (Assume the disc has negligible mass.)

What is the radius of gyration? Write its unit and dimensional formula.

The moment of inertia of a solid disc rotating about its diameter is $2.5$ times higher than the moment of inertia of a ring rotating in a similar way. The moment of inertia of a solid sphere which has the same radius as the disc and is rotating in a similar way,is $n$ times higher than the moment of inertia of the given ring. Here,$n=$ . . . . . . . Consider all the bodies have equal masses.