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(D) The frequency of oscillation in a vibration magnetometer is given by $f = \frac{1}{2\pi} \sqrt{\frac{mB_H}{I}}$.When like poles are together,the e

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$5 : 4$

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(D) The frequency of oscillation in a vibration magnetometer is given by $f = \frac{1}{2\pi} \sqrt{\frac{mB_H}{I}}$.When like poles are together,the effective magnetic moment is $M_1 = m_1 + m_2$ and the frequency is $f_1 = 12 	ext{ oscillations/min}$.When unlike poles are together,the effective magnetic moment is $M_2 = m_1 - m_2$ and the frequency is $f_2 = 4 	ext{ oscillations/min}$.Since $f \propto \sqrt{M}$,we have $\frac{f_1}{f_2} = \sqrt{\frac{m_1 + m_2}{m_1 - m_2}}$.Substituting the values: $\frac{12}{4} = \sqrt{\frac{m_1 + m_2}{m_1 - m_2}} \implies 3 = \sqrt{\frac{m_1 + m_2}{m_1 - m_2}}$.Squaring both sides: $9 = \frac{m_1 + m_2}{m_1 - m_2}$.$9m_1 - 9m_2 = m_1 + m_2 \implies 8m_1 = 10m_2$.Therefore,$\frac{m_1}{m_2} = \frac{10}{8} = \frac{5}{4}$.

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