The frequency of vibration in a vibration mag | vedclass

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(B) The frequency of oscillation in a vibration magnetometer is given by $n = \frac{1}{2\pi} \sqrt{\frac{MB}{I}}$.For two magnets with moments $M_1$ a

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$5: 4$

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(B) The frequency of oscillation in a vibration magnetometer is given by $n = \frac{1}{2\pi} \sqrt{\frac{MB}{I}}$.For two magnets with moments $M_1$ and $M_2$ and moment of inertia $I_1$ and $I_2$, when tied together, the total moment of inertia is $I = I_1 + I_2$.When like poles are tied, the effective magnetic moment is $M_{sum} = M_1 + M_2$. The frequency is $n_1 = 6 \ Hz$.When unlike poles are tied, the effective magnetic moment is $M_{diff} = M_1 - M_2$. The frequency is $n_2 = 2 \ Hz$.Since $n \propto \sqrt{M}$, we have $\frac{n_1}{n_2} = \sqrt{\frac{M_1 + M_2}{M_1 - M_2}}$.Squaring both sides: $(\frac{6}{2})^2 = \frac{M_1 + M_2}{M_1 - M_2} \implies 9 = \frac{M_1 + M_2}{M_1 - M_2}$.$9M_1 - 9M_2 = M_1 + M_2$.$8M_1 = 10M_2$.$\frac{M_1}{M_2} = \frac{10}{8} = \frac{5}{4}$.

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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