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(B) The frequency of oscillation $v$ in a vibration magnetometer is given by $v = \frac{1}{2\pi} \sqrt{\frac{MB}{I}}$.When magnets are placed together

Vedclass · Accepted Answer

$25:7$

Vedclass · Answer

(B) The frequency of oscillation $v$ in a vibration magnetometer is given by $v = \frac{1}{2\pi} \sqrt{\frac{MB}{I}}$.When magnets are placed together,the effective magnetic moment $M_{eff}$ is $(M_A + M_B)$ for similar poles and $(M_A - M_B)$ for opposite poles.Let $v_s = 20 	ext{ oscillations/min}$ (similar poles) and $v_d = 15 	ext{ oscillations/min}$ (opposite poles).Since $v \propto \sqrt{M}$,we have $\frac{v_s}{v_d} = \sqrt{\frac{M_A + M_B}{M_A - M_B}}$.Squaring both sides: $\left(\frac{20}{15}ight)^2 = \frac{M_A + M_B}{M_A - M_B} \Rightarrow \left(\frac{4}{3}ight)^2 = \frac{M_A + M_B}{M_A - M_B}$.$\frac{16}{9} = \frac{M_A + M_B}{M_A - M_B}$.Applying componendo and dividendo: $\frac{M_A}{M_B} = \frac{16+9}{16-9} = \frac{25}{7}$.Thus,the ratio $M_A : M_B = 25:7$.

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