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Q.

The ratio of magnetic moments of two bar magnets is 13 : 5.These magnets held together in a vibration magnetometer, are allowed to oscillate in earth's magnetic field with like poles together such that 15 oscillations per minute are made. What will be the frequency of oscillation of system if unlike poles are together?

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a

10 oscillations/min

b

15 oscillations/min

c

12 oscillations/min

d

$\frac{75}{13}$ oscillations/min

answer is A.

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Detailed Solution

$\begin{array}{rcl} ϑ_{s} & = & \frac{1}{2 π} \sqrt{\frac{(M_{1} + M_{2}) B_{H}}{I}} \\ ϑ_{d} & = & \frac{1}{2 π} \sqrt{\frac{(M_{1} - M_{2}) B_{H}}{I}} \\ \frac{M_{1}}{M_{2}} = \frac{{ϑ_{s}}^{2} + {ϑ_{d}}^{2}}{{ϑ_{s}}^{2} - {ϑ_{d}}^{2}} \Rightarrow \frac{13}{5} = \frac{{(15)}^{2} + {ϑ_{d}}^{2}}{{(15)}^{2} - {ϑ_{d}}^{2}} \end{array}$

$\Rightarrow ϑ_{d}$ = 10 oscillations/min

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