A combination of two bar magnets, in vibration magnetometer, makes $10$ oscillations per second if their like poles are tied together and $2$ oscillations per second when unlike poles are tied together. If induced magnetism is neglected, then the ratio of their magnetic moments is

\frac{3}{2}

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\frac{13}{12}

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\frac{8}{9}

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\frac{12}{11}

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Solution

The correct option is C $\frac{13}{12}$
From the given data, we can figure out that $T_{1} = \frac{1}{2} = 0.5 s$ and $T_{2} = \frac{1}{10} = 0.1 s$

$∴ \frac{M_{1}}{M_{2}} = \frac{T_{1}^{2} + T_{2}^{2}}{T_{2}^{2} - T_{1}^{2}} = \frac{(0.5)^{2} + (0.1)^{2}}{(0.5)^{2} - (0.1)^{2}} = \frac{.25 + .01}{.25 - .01} = \frac{13}{12}$

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A combination of two bar magnets, in vibration magnetometer, makes 10 oscillations per second if their like poles are tied together and 2 oscillations per second when unlike poles are tied together. If induced magnetism is neglected, then the ratio of their magnetic moments is

The correct option is C 1312From the given data, we can figure out that T1=12=0.5s and T2=110=0.1s∴M1M2=T21+T22T22−T21=(0.5)2+(0.1)2(0.5)2−(0.1)2=.25+.01.25−.01=1312

A combination of two bar magnets, in vibration magnetometer, makes $10$ oscillations per second if their like poles are tied together and $2$ oscillations per second when unlike poles are tied together. If induced magnetism is neglected, then the ratio of their magnetic moments is