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

The oxygen molecule has a mass of 5.30 x 10^-26 kg and a moment of inertia of 1.94 x 10^-46 kg m² 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 m/s and that its kinetic energy of rotation is two-thirds of its kinetic energy of translation. Find the average angular velocity of the molecule.

1. $5.7\times {10}^{11} rad s^{-1}$

2. $5.7\times {10}^{12} rad s^{-1}$

3. $6.7\times {10}^{11} rad s^{-1}$

4.$6.7\times {10}^{12} rad s^{-1}$