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

Answer 1

The correct option is C $6.65s$

Time period of oscillation $=2\pi \sqrt{\frac{I}{BM}}$
where, $I$ is moment of inertia of the needle
$B$ is the magnetic field
$M$ is the magnetic moment
So,
Time taken for $10$ oscillations $=10T$
$=20\pi \sqrt{\frac{I}{BM}}$
$=20\pi \sqrt{\frac{7.5\times {10}^{-6}kg{m}^2}{\left(0.01T\right)(6.7\times {10}^{-2}A{m}^2)}}$
$=6.65s$
Option $C$ is correct.