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Two bar magnets of the same length and breadth but having magnetic moments M and 2M are joined with like poles together and suspended by a string. The time of oscillation of this assembly in a magnetic field of strength ‘B’ is 3 sec. What will be the period of oscillation, if the polarity of one of the magnets is changed and the combination is again made to oscillate in the same field?

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$\frac{1}{\sqrt{3}} \sec$

$\frac{1}{3 \sqrt{3}} \sec$

$3 \sqrt{3} \sec$

$\sqrt{3} \sec$

answer is B.

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Detailed Solution

When magnets are joined with like poles together

$M_{1} = M + 2 M = 3 M$

$T = 2 π \sqrt{\frac{(I_{1} + I_{2})}{3 M B}} \to (1)$

When the polarity of one of the magnet is reversed,

$M_{2} = M ~ 2 M = M$

$So, T^{1} = 2 π \sqrt{\frac{(I_{1} + I_{2})}{M B}} \to (2)$

From (1) & (2)

$\frac{T^{1}}{T} = \sqrt{3}, i.e., T^{1} = 3 \sqrt{3} Sec$

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