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

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6.65

8.89

9.98

8.76

answer is A.

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Detailed Solution

$T = 2 π \sqrt{\frac{I}{M B}}$

Time for 10 oscillations is

$t = 10 T$

$\begin{array}{l} T = \frac{2 π}{ω} = 2 π \sqrt{\frac{I}{mB}} \\ = 10 \times 2 π \sqrt{\frac{I}{mB}} \\ = 10 \times 2 \times 3.14 \times \sqrt{\frac{7.6 \times 10^{- 6}}{6.7 \times 10^{- 2} \times 0.01}} \\ = 6.65 s \end{array}$

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