Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of 3 s a

Question

Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of 3 s and 4 s respectively. If their moments of inertia are in the ratio of $3: 2$, then the ratio of their magnetic moments will be\

Professor PC Thomas Classes · Answer

(b) : Time period of oscillation of a magnet in a magnetic field $B$ is,\ $T=2 \pi \sqrt{\frac{I}{M B}}$\ where $I$ and $M$ are the moment of inertia and the magnetic moment of the magnet respectively.\ $	herefore \frac{T_{1}}{T_{2}}=\sqrt{\frac{I_{1}}{I_{2}} 	imes \frac{M_{2}}{M_{1}}}$\ $\Rightarrow \frac{3}{4}=\sqrt{\frac{I_{1}}{I_{2}}} 	imes \sqrt{\frac{M_{2}}{M_{1}}}=\sqrt{\frac{3}{2}} 	imes \sqrt{\frac{M_{2}}{M_{1}}}$\ or $\frac{9}{16}=\frac{3}{2} 	imes \frac{M_{2}}{M_{1}}$ or $\frac{M_{1}}{M_{2}}=\frac{8}{3}$\