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Two magnets of magnetic moments M and 2M are placed in a vibration magnetometer, with the identical poles in the same direction. The time period of vibration is $T_{1} .$ If the magnets are placed with opposite poles together and vibrate with time period $T_{2},$ then

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$T_{2} < T_{1}$

$T_{2},$ is infinite

$T_{2} = T_{1}$

$T_{2} > T_{1}$

answer is C.

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Detailed Solution

$T_{1} = 2 π \sqrt{\frac{I_{1} + I_{2}}{(M + 2 M) H}} = 2 π \sqrt{\frac{I}{3 MH}}$

$T_{2} = 2 π \sqrt{\frac{I_{1} + I_{2}}{(2 M - M) H}} = 2 π \sqrt{\frac{I}{MH}}$

Obviously, $T_{2} > T_{1}$

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