Time periods of vibration of two bar magnets in sum and difference positions are $4$ sec and $6$ sec respectively. The ratio of their magnetic moments $M_{1} / M_{2}$ is

6 : 4

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30 : 16

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2.6 : 1

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1.5 : 1

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Solution

The correct option is C $2.6 : 1$
$\frac{M_{1}}{M_{2}} = \frac{T_{2}^{2} + T_{1}^{2}}{T_{2}^{2} - T_{1}^{2}}$
$= \frac{6^{2} + 4^{2}}{6^{2} - 4^{2}}$
$= \frac{52}{20} = (2.6) : 1$

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