One bar magnet is in simple harmonic motion with time period T in an earth's magnetic field. If its mass is…
One bar magnet is in simple harmonic motion with time period T in an earth's magnetic field. If its mass is increased by 9 times the time period becomes
3T
9T
4T
$\sqrt{3} \mathrm{~T}$
Solution
The time period of a bar magnet in a magnetic field is
$\begin{aligned}
& \mathrm{T}=2 \pi \sqrt{\frac{\mathrm{I}}{\mathrm{MB}}}=2 \pi \sqrt{\frac{\mathrm{mk}^2}{\mathrm{MB}}} \Rightarrow \mathrm{~T} \propto \sqrt{\mathrm{~m}} \\
& \therefore \frac{\mathrm{~T}_2}{\mathrm{~T}_1}=\sqrt{\frac{\mathrm{m}_2}{\mathrm{~m}_1}}=\sqrt{\frac{9 \mathrm{~m}_1}{\mathrm{~m}_1}}=3 \\
& \therefore \quad \mathrm{~T}_2=3 \mathrm{~T}_1=3 \mathrm{~T}
\end{aligned}$