Question

A magnetic needle has magnetic moment $6.7 \times 10^{-2}$ $Am ^{2}$ and moment of inertia $=7.5 \times 10^{-6} kg m ^{2} .$ If it performs 10 complete oscillations in 6.70 sec. What is the magnitude of magnetic field?

• A. $9.89 \times 10^{-2} T$
• B. $9.852 \times 10^{-3} T$
• C. $10 \times 10^{-5} T$
• D. $12\, T$

Answer 1

Answer: (B)

As we know $T=2 \pi \sqrt{\frac{I}{M B}}$
$ B =4 \pi^{2} \times \frac{ I }{ MT ^{2}} $
$=4 \times \frac{22}{7} \times \frac{22}{7} \times \frac{7.5 \times 10^{-6}}{6.7 \times 10^{-2} \times(0.67)^{2}} $
$=4 \times\left(\frac{22}{7}\right)^{2} \times \frac{7.5 \times 10^{-6}}{6.7 \times 10^{-2} \times(0.67)^{2}} $
$ B =9.852 \times 10^{-3} T $