The ratio of magnetic moments of two bar magn | vedclass

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Question

(A) Let the magnetic moments be $M_1$ and $M_2$ such that $\frac{M_1}{M_2} = \frac{13}{5}$.When like poles are together,the effective magnetic moment

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$10$

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(A) Let the magnetic moments be $M_1$ and $M_2$ such that $\frac{M_1}{M_2} = \frac{13}{5}$.When like poles are together,the effective magnetic moment is $M_s = M_1 + M_2$ and the frequency is $
u_s = 15 	ext{ oscillations/min}$.When unlike poles are together,the effective magnetic moment is $M_d = M_1 - M_2$ and the frequency is $
u_d$.The frequency of a vibration magnetometer is given by $
u \propto \sqrt{M}$.Therefore,$\frac{
u_s}{
u_d} = \sqrt{\frac{M_1 + M_2}{M_1 - M_2}}$.Squaring both sides: $\frac{
u_s^2}{
u_d^2} = \frac{M_1 + M_2}{M_1 - M_2} = \frac{13 + 5}{13 - 5} = \frac{18}{8} = \frac{9}{4}$.Taking the square root: $\frac{
u_s}{
u_d} = \frac{3}{2}$.Given $
u_s = 15$,we have $\frac{15}{
u_d} = \frac{3}{2}$.Solving for $
u_d$: $
u_d = \frac{15 	imes 2}{3} = 10 	ext{ oscillations/min}$.

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