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 :

Updated On: Jul 8, 2024
  • 6.65 s
  • 8.89 s
  • 6.98 s
  • 8.76 s
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The Correct Option is A

Solution and Explanation

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, 
\(t = 10\,T = 2\pi \times1.06\)
\(= 6.6568 \approx6.65\, s\)
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Magnets are used in many devices like electric bells, telephones, radio, loudspeakers, motors, fans, screwdrivers, lifting heavy iron loads, super-fast trains, especially in foreign countries, refrigerators, etc.

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