Question

A magnetic needle of magnetic moment $6.7 \times 10^{-2} \, Am^2$ and moment of inertia $7.5 \times 10^{-6} \, kg \, m^2$ is performing simple harmonic oscillations in a magnetic field of $0.01\, T$. Time taken for $10$ complete oscillations is :

• A. 6.65 s
• B. 8.89 s
• C. 6.98 s
• D. 8.76 s

Answer 1

Answer: (A)

6.65 s

Answer 2

The correct option is(A): 6.65 s
$T = 2 \pi \sqrt{\frac{I}{MB}}$
$= 2\pi \sqrt{\frac{7.5 \times10^{-6}}{6.7 \times10^{-2} \times0.01}} = \frac{2\pi}{10} \times1.06$
For 10 oscillations,
$t = 10\,T = 2\pi \times1.06$
$= 6.6568 \approx6.65\, s$