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
8.76s
B
6.65s
C
8.89s
D
6.98s

Solution

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

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