A magnetic needle of magnetic moment $6 \times 10^{-2} \mathrm{Am}^2$ and moment of inertia $9.6 \times…
A magnetic needle of magnetic moment $6 \times 10^{-2} \mathrm{Am}^2$ and moment of inertia $9.6 \times 10^{-5} \mathrm{~kg} \mathrm{~m}^2$ performs simple harmonic motion in a magnetic field of 0.01 T . Time taken to complete 10 oscillations is [Take $\pi=3 \cdot 14$ ]
0.2512 s
2.512 s
25.12 s
$251 \cdot 2 \mathrm{~s}$
Solution
Period of oscillation $T=2 \pi \sqrt{\frac{\mathrm{I}}{\mathrm{MB}}}$
$\begin{aligned}
& =2 \pi \sqrt{\frac{9.6 \times 10^{-5}}{6 \times 10^{-2} \times 0.01}} \\
& =2.512 \mathrm{~s}
\end{aligned}$
$\therefore \quad$ Time taken for 10 oscillations $=2.512 \times 10$
$=25.12 \mathrm{~s}$