Question

A bar-magnet of moment of inertia $49 \times 10^{-2}\, kg - m ^{2}$ vibrates in a magnetic field of induction $0.5 \times 10^{-4} T$. The time period of vibration is $8.8\, s$. The magnetic moment of the bar magnet is

• A. $350\, A - m ^{2}$
• B. $490\, A - m ^{2}$
• C. $3300\, A - m ^{2}$
• D. $5000\, A - m ^{2}$

Answer 1

Answer: (D)

Time period of magnet is
$T=2 \pi \sqrt{\frac{I}{M H}}$
or $M= \frac{4 \pi^{2} I}{T^{2} H}$
or $M=\frac{4 \times(3.14)^{2} \times 49 \times 10^{-2}}{(8.8)^{2} \times 0.5 \times 10^{-4}}$
or $M=5000\, A - m ^{2}$