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Q.

Two bar magnets oscillate in a horizontal plane in earth’s magnetic field with time periods of 3 s and 4 s respectively. If their moments of inertia are in the ratio of 3 : 2 then the ratio of their magnetic moments will be :

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a

2 : 1

b

8 : 3

c

1 : 3

d

27 : 16

answer is B.

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Detailed Solution

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$\begin{array}{l} T = 2 π \sqrt{\frac{I}{{MB}_{H}}} \\ \frac{T_{1}}{T_{2}} = \frac{2 π \sqrt{\frac{I_{1}}{M_{1} B_{H}}}}{2 π \sqrt{\frac{I_{2}}{M_{2} B_{H}}}} = \frac{3}{4} \\ \sqrt{\frac{I_{1}}{I_{2}} \times \frac{M_{2}}{M_{1}}} = \frac{3}{4} \\ \sqrt{\frac{I_{1}}{I_{2}}} \times \sqrt{\frac{M_{2}}{M_{1}}} = \frac{3}{4} \\ \sqrt{\frac{3}{2}} \times \sqrt{\frac{M_{2}}{M_{1}}} = \frac{3}{4} \\ \frac{3}{2} \times \frac{M_{2}}{M_{1}} = \frac{9}{16} \\ \frac{M_{1}}{M_{2}} = \frac{8}{3} \end{array}$

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Two bar magnets oscillate in a horizontal plane in earth’s magnetic field with time periods of 3 s and 4 s respectively. If their moments of inertia are in the ratio of 3 : 2 then the ratio of their magnetic moments will be :