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(D) The time period of a vibrating magnet is given by $T = 2\pi \sqrt{\frac{I}{MB_H}}$.This implies $T \propto \frac{1}{\sqrt{B_H}}$.Given at the firs

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$\sqrt{2} ~s$

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(D) The time period of a vibrating magnet 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,$n_1 = 30 	ext{ oscillations/min} = 0.5 	ext{ oscillations/s}$.Therefore,the time period $T_1 = \frac{1}{n_1} = \frac{1}{0.5} = 2 ~s$.At the second place,the magnetic field is doubled,so $(B_H)_2 = 2(B_H)_1$.The ratio of time periods is $\frac{T_2}{T_1} = \sqrt{\frac{(B_H)_1}{(B_H)_2}} = \sqrt{\frac{(B_H)_1}{2(B_H)_1}} = \frac{1}{\sqrt{2}}$.Thus,$T_2 = T_1 	imes \frac{1}{\sqrt{2}} = 2 	imes \frac{1}{\sqrt{2}} = \sqrt{2} ~s$.

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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