Given the moment of inertia of a disc of mass \(M\) and radius \(R\) about any of its diameters to be \(\dfrac{MR^{2}}{4},\) then the moment of inertia about an axis normal to the disc passing through a point on its edge is:
1. \(\dfrac{3}{2}MR^{2}\)
2. \(\dfrac{1}{4}MR^{2}\)
3. \(\dfrac{2}{5}MR^{2}\)
4. \(\dfrac{7}{5}MR^{2}\)

The oxygen molecule has a mass of \(5.30\times 10^{-26}~\text{kg}\) and a moment of inertia of \(1.94\times 10^{-46}~\text{kg m}^2\) about an axis through its center perpendicular to the lines joining the two atoms. Suppose the mean speed of such a molecule in a gas is \(500~\text{m/s}\) and that its kinetic energy of rotation is two-thirds of its kinetic energy of translation. The average angular velocity of the molecule is:
1. \(5.7\times 10^{11}~\text{rad/s}\)
2. \(5.7\times 10^{12}~\text{rad/s}\)
3. \(6.7\times 10^{11}~\text{rad/s}\)
4. \(6.7\times 10^{12}~\text{rad/s}\)