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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
8.76s
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B
6.65s
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C
8.89s
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D
6.98s
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Solution

The correct option is B $$6.65\, s$$
$$T=mB \sin \theta = I\dfrac{d^2\theta}{dt^2}$$
$$mB\theta = I\dfrac{d^2\theta}{dt^2}$$
$$\Rightarrow \omega = \sqrt{\dfrac{mB}{I}}$$
$$T=\dfrac{2\pi}{\omega}=2\pi \sqrt{\dfrac{I}{mB}}$$
$$=10\times 2\pi \sqrt{\dfrac{I}{mB}}$$
$$=10\times 2\times 3.14\times \sqrt{\dfrac{7.6\times 10^{-6}}{6.7\times 10^{-2}\times 0.01}}$$
$$=6.65 s$$

Physics
NCERT
Standard XII

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