Two bar magnets are placed in a vibration magnetometer and allowed to vibrate. They make $20$ oscillations per minute when their similar poles are on the same side, while they make $15$ oscillations per minute when their opposite poles lie on the same side. The ratio of their magnetic moments is
Answer: (B) $25 : 7$
Concept. In a vibration magnetometer $f = \dfrac{1}{2\pi}\sqrt{\dfrac{MB}{I}}$. The combination has the same moment of inertia in both arrangements, so $f^2 \propto M$.
Step 1. Net moments. Similar poles on the same side: $M_1 + M_2$. Opposite poles on the same side: $M_1 - M_2$.
Step 2. Ratio of frequencies.
$$\frac{M_1 + M_2}{M_1 - M_2} = \frac{20^2}{15^2} = \frac{16}{9}$$
Step 3. Solve. $9M_1 + 9M_2 = 16M_1 - 16M_2 \Rightarrow 7M_1 = 25M_2$, so $\dfrac{M_1}{M_2} = \dfrac{25}{7}$.
Answer. $25 : 7$ (Option B).
Solution by Sreeraj P, M.Sc Physics