The frequency of vibration in a vibration mag | vedclass

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(B) The frequency of vibration in a vibration magnetometer is given by $n = \frac{1}{2\pi} \sqrt{\frac{MB}{I}}$.For the combination of two magnets,the

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$5: 4$

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(B) The frequency of vibration in a vibration magnetometer is given by $n = \frac{1}{2\pi} \sqrt{\frac{MB}{I}}$.For the combination of two magnets,the effective magnetic moment $M_{eff}$ and moment of inertia $I_{eff} = I_1 + I_2$ are used.When like poles are tied together,$M_{eff} = M_1 + M_2$,so $n_1 = \frac{1}{2\pi} \sqrt{\frac{(M_1+M_2)B}{I_1+I_2}} = 6 ~Hz$.When unlike poles are tied together,$M_{eff} = M_1 - M_2$,so $n_2 = \frac{1}{2\pi} \sqrt{\frac{(M_1-M_2)B}{I_1+I_2}} = 2 ~Hz$.Taking the ratio of the two frequencies:$\frac{n_1}{n_2} = \sqrt{\frac{M_1+M_2}{M_1-M_2}} = \frac{6}{2} = 3$.Squaring both sides:$\frac{M_1+M_2}{M_1-M_2} = 9$.$M_1 + M_2 = 9M_1 - 9M_2$.$10M_2 = 8M_1$.$\frac{M_1}{M_2} = \frac{10}{8} = \frac{5}{4}$.Thus,the ratio $M_1: M_2$ is $5: 4$.

The frequency of vibration in a vibration magnetometer of the combination of two bar magnets of magnetic moments $M_1$ and $M_2$ is $6 ~Hz$ when like poles are tied together and it is $2 ~Hz$ when the unlike poles are tied together,then the ratio $M_1: M_2$ is

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