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Two magnets of magnetic moments M and 2M are placed in a vibration magnetometer, with the identical poles in the same direction. The time period of vibration is T₁. If the magnets are placed with opposite poles together and vibrate with time period T₂, then

1. T₂ is infinite
2. T₂ = T₁
3. T₂ > T₁
4. T₂ < T₁

Correct answer: T₂ < T₁

Solution

When the magnets are placed with identical poles in the same direction, their magnetic moments add up, resulting in a net magnetic moment of 3M. When placed with opposite poles together, their magnetic moments subtract, resulting in a net magnetic moment of M. Since the time period of vibration is inversely proportional to the square root of the magnetic moment, T₂ (for net moment M) will be greater than T₁ (for net moment 3M). Thus, T₂ < T₁.

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