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(D) The time period of a magnetic dipole oscillating in a magnetic field is given by $T = 2\pi \sqrt{\frac{I}{MB_H}}$.This implies $T \propto \frac{1}

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$\sqrt{2} \, 	ext{sec}$

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(D) The time period of a magnetic dipole oscillating in a magnetic field is given by $T = 2\pi \sqrt{\frac{I}{MB_H}}$.This implies $T \propto \frac{1}{\sqrt{B_H}}$.Given at the first place,$n_1 = 30 \, 	ext{oscillations/min} = 0.5 \, 	ext{Hz}$.Thus,the time period $T_1 = \frac{1}{n_1} = \frac{1}{0.5} = 2 \, 	ext{sec}$.Let the magnetic field at the first place be $B_H$. Then at the second place,the magnetic field is $2B_H$.Using the relation $\frac{T_2}{T_1} = \sqrt{\frac{B_{H1}}{B_{H2}}}$,we get:$T_2 = T_1 \sqrt{\frac{B_H}{2B_H}} = 2 	imes \frac{1}{\sqrt{2}} = \sqrt{2} \, 	ext{sec}$.

At a certain place,a magnet makes $30$ oscillations per minute. At another place where the magnetic field is double,its time period will be:

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