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Current Loop Is a Magnet?

A magnetic ne...

Question

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

6.98 s

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8.76 s

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6.65 s

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8.89 s

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Solution

The correct option is C $6.65 s$
Time period of oscillation $= 2 π \sqrt{\frac{I}{B M}}$
where, $I$ is moment of inertia of the needle
$B$ is the magnetic field
$M$ is the magnetic moment
So,
Time taken for $10$ oscillations $= 10 T$
$= 20 π \sqrt{\frac{I}{B M}}$
$= 20 π \sqrt{\frac{7.5 \times 10^{- 6} k g m^{2}}{(0.01 T) (6.7 \times 10^{- 2} A m^{2})}}$
$= 6.65 s$
Option $C$ is correct.

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