Question

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

• A. $8.76s$
• B. $6.65s$
• C. $8.89s$
• D. $6.98s$

Answer 1

The correct option is B $6.65s$

$T=mB\sin \theta =I\frac{d^2\theta }{d{t}^2}$

$mB\theta =I\frac{d^2\theta }{d{t}^2}$

$\Rightarrow \omega =\sqrt{\frac{mB}{I}}$

$T=\frac{2\pi }{\omega }=2\pi \sqrt{\frac{I}{mB}}$

$=10\times 2\pi \sqrt{\frac{I}{mB}}$

$=10\times 2\times 3.14\times \sqrt{\frac{7.6\times {10}^{-6}}{6.7\times {10}^{-2}\times 0.01}}$

$=6.65s$