The length, breadth and mass of two bar magnets are same but their magnetic moments are 3M and 2M respectively. These are joined in parallel with similar poles on same side and are suspended by a string. When oscillated in a magnetic field of strength $B,$ the time period obtained is $5 s .$ If the poles of either of the magnets are reversed then the time period of the combination in the same magnetic field will be

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$2 \sqrt{2} s$

$5 \sqrt{5} s$

$1 s$

$3 \sqrt{3} s$

answer is B.

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Detailed Solution

From $T = 2 π \sqrt{\frac{I}{M B}}, T \propto \frac{1}{\sqrt{M}}$

Joining pole to pole means sum position, then $\frac{T_{2}}{T_{1}} = \sqrt{\frac{M_{1} + M_{2}}{M_{1} - M_{2}}} = \sqrt{\frac{3 M + 2 M}{3 M - 2 M}} = \sqrt{5}$

$T_{2} = \sqrt{5} \times T_{1} = \sqrt{5} \times 5 s$

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