A bar magnet of moment of inertia $9 imes 10^{-5} \mathrm{~kg} \mathrm{~m}^{2}$ placed in a vibrat

Question

A bar magnet of moment of inertia $9 	imes 10^{-5} \mathrm{~kg} \mathrm{~m}^{2}$ placed in a vibration magnetometer and oscillating in a uniform magnetic field\ $16 \pi^{2} 	imes 10^{-5} \mathrm{~T}$ makes 20 oscillations in 15 s . The magnetic moment of the bar magnet is\

Professor PC Thomas Classes · Answer

In a vibration magnetometer Time period, $\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{I}}{\mathrm{MB}}}$\ Where the symbols have their usual meanings.\ or $\frac{4 \pi^{2} \mathrm{I}}{\mathrm{BT}^{2}}$\ Here, $\mathrm{I}=9 	imes 10^{-5} \mathrm{kgm}^{2}, \mathrm{~B}=16 \pi^{2} 	imes 10^{-5} \mathrm{~T}$\ $\mathrm{T}=\frac{15}{20}=\frac{3}{4} \mathrm{~s}$\ $	herefore \mathrm{M}=\frac{4 \pi^{2} 	imes 9 	imes 10^{-5}}{16 \pi^{2} 	imes 10^{-5} 	imes\left(\frac{3}{4}ight)^{2}}=4 \mathrm{Am}^{2}$\