A short bar magnet having magnetic moment $4\;Am^2,$ placed in a vibrating magnetometer, vibrates with a time period of 8 seconds. Another short bar magnet having a magnetic moment $8\;Am^2$ vibrates with a time period of $6$ seconds. If the moment of inertia of the second magnet is $9 \times 10^{-2}\;kg\;m^2,$ the moment of inertia of the first magnet is (Assume that both magnets are kept in the same uniform magnetic induction field.)

Question

\[(a)\;9 \times 10^{-2}\;kg\;m^2 \quad (b)\;8 \times 10^{-2}\;kg\;m^2 \quad (c)\;5.33 \times 10^{-2}\;kg\;m^{-2} \quad (d)\;12.2 \times 10^{-2}\;kg\;m^2 \]