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 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,
\(t = 10\,T = 2\pi \times1.06\)
\(= 6.6568 \approx6.65\, s\)
\(T = 2 \pi \sqrt{\frac{I}{MB}}\)
\(= 2\pi \sqrt{\frac{7.5 \times10^{-6}}{6.7 \times10^{-2} \times0.01}} = \frac{2\pi}{10} \times1.06\)
For 10 oscillations,
\(t = 10\,T = 2\pi \times1.06\)
\(= 6.6568 \approx6.65\, s\)
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Magnetite is the world’s first magnet. This is also called a natural magnet. Though magnets occur naturally, we can also impart magnetic properties to a substance. It would be an artificial magnet in that case.
Read More: Magnetism and Matter
Some of the properties of the magnetic field lines are:
- The lines and continuous and outside the magnet, the field lines originate from the North pole and terminate at the South pole
- They form closed loops traversing inside the magnet.
- But here the lines seem to originate from the South pole and terminate at the North pole to form closed loops.
- More number of close lines indicate a stronger magnetic field
- The lines do not intersect each other
- The tangent drawn at the field line gives the direction of the field at that point.