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  4. A magnetic needle of magnetic moment 6.7 × 10-2 Am2 and moment of inertia 7.5 × 10-6 kg m2 is performing simple harmonic oscillations in a magnetic field of 0.01 T. Time taken for 10 complete oscillations is :

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Q. 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 :

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Solution:

$T = 2 \pi \sqrt{\frac{I}{MB}}$
$ = 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 $