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(D) In a vibration magnetometer,the frequency of oscillation $n$ is given by $n = \frac{1}{2\pi} \sqrt{\frac{MB}{I}}$.For two magnets with magnetic mo

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$5:4$

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(D) In a vibration magnetometer,the frequency of oscillation $n$ is given by $n = \frac{1}{2\pi} \sqrt{\frac{MB}{I}}$.For two magnets with magnetic moments $M_1$ and $M_2$ and moments of inertia $I_1$ and $I_2$,the combined frequency $n$ is proportional to $\sqrt{M_{eff}}$.When like poles are together,$M_{eff} = M_1 + M_2$,so $n_1 \propto \sqrt{M_1 + M_2}$.When unlike poles are together,$M_{eff} = M_1 - M_2$,so $n_2 \propto \sqrt{M_1 - M_2}$.Given $n_1 = 12$ and $n_2 = 4$,we have $\frac{n_1}{n_2} = \frac{12}{4} = 3$.Thus,$\frac{\sqrt{M_1 + M_2}}{\sqrt{M_1 - M_2}} = 3$.Squaring both sides,$\frac{M_1 + M_2}{M_1 - M_2} = 9$.$M_1 + M_2 = 9M_1 - 9M_2$.$10M_2 = 8M_1$.$\frac{M_1}{M_2} = \frac{10}{8} = \frac{5}{4}$.

Two magnets are held together in a vibration magnetometer and are allowed to oscillate in the earth's magnetic field. With like poles together,$12$ oscillations per minute are made,but for unlike poles together,only $4$ oscillations per minute are executed. The ratio of their magnetic moments is:

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