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Two small magnets have their masses and lengths in the ratio 2 : 4. The maximum torques experienced by them in a uniform magnetic field are the same. For small oscillations, the ratio of their periods is

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$\frac{1}{2 \sqrt{2}}$

$\frac{1}{\sqrt{2}}$

$(\frac{1}{2})$

$2 \sqrt{2}$

answer is A.

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Detailed Solution

$T = 2 π \sqrt{\frac{I}{MB}}$

$\frac{T_{1}}{T_{2}} = \sqrt{\frac{m_{1}}{m_{2}} \times {(\frac{l_{1}}{l_{2}})}^{2}}$

$= \sqrt{\frac{2}{4} \times \frac{2^{2}}{4^{2}}} = \frac{1}{2 \sqrt{2}}$

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