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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 oscillation in a magnetic field of 0.01 T time taken for 10 complete oscillation is

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6.98 sec

8.76 sec

6.65 sec

8.89 sec

answer is C.

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Detailed Solution

$M = 6.7 \times 10^{- 12} A m^{2}$

$\begin{array}{l} B = 0.01 T \\ I = 7.5 \times 10^{- 6} k g m^{2} \\ T = 2 π \sqrt{\frac{I}{M B}} \\ T = 2 π \sqrt{\frac{7.5 \times 10^{- 6}}{6.7 \times 10^{- 12} \times 0.01}} = \frac{2 π}{10} \times 1.06 \sec \end{array}$

Time taken for 10 complete oscillations

$\begin{array}{l} t = 10 T = 2 π \times 1.06 \\ = 6.65 \sec \end{array}$

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