Two bar magnets ' \(\mathrm{P}\) ' and ' \(\mathrm{Q}\) ' are kept in uniform magnetic field 'B' with magnetic moments ' \(\mathrm{M}_{\mathrm{P}}\) ' and ' \(\mathrm{M}_{\mathrm{Q}}\) ' respectively. Magnet ' \(\mathrm{P}\) ' is oscillating with frequency twice that of magnet ' \(\mathrm{Q}\) '. If the moment of inertia of the magnet ' \(\mathrm{P}\) ' is twice that of magnet ' \(\mathrm{Q}\) ' then

The frequency of oscillation given by
\(\begin{aligned}
& \mathrm{f}_{\mathrm{p}}=\frac{1}{2 \pi} \sqrt{\frac{\mathrm{M}_{\mathrm{p}} \mathrm{B}}{\mathrm{I}_P}} \text { and } \mathrm{f}_{\mathrm{Q}}=\frac{1}{2 \pi} \sqrt{\frac{\mathrm{M}_{\mathrm{Q}} \mathrm{B}}{\mathrm{I}_{\mathrm{Q}}}} \\
& \mathrm{f}_{\mathrm{p}}=2 \mathrm{f}_{\mathrm{Q}} \\
& \frac{1}{2 \pi} \sqrt{\frac{\mathrm{M}_{\mathrm{P}} \mathrm{B}}{\mathrm{I}_{\mathrm{P}}}}=2 \cdot \frac{1}{2 \pi} \sqrt{\frac{\mathrm{M}_{\mathrm{Q}} \mathrm{B}}{\mathrm{I}_{\mathrm{Q}}}} \\
& \frac{\mathrm{M}_{\mathrm{P}}}{\mathrm{I}_{\mathrm{P}}}=4 \frac{\mathrm{M}_{\mathrm{Q}}}{\mathrm{I}_{\mathrm{Q}}} \\
& \therefore \frac{\mathrm{M}_{\mathrm{P}}}{\mathrm{M}_{\mathrm{Q}}}=4 \frac{\mathrm{I}_{\mathrm{P}}}{\mathrm{I}_{\mathrm{Q}}}=8 \quad\left[\because \mathrm{I}_{\mathrm{P}}=2 \mathrm{I}_{\mathrm{Q}}\right]
\end{aligned}\)