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A bar magnet has a length much greater than its width and thickness. In a vibration magnetometer, it oscillates with a period of 2 s. The magnet is then divided lengthwise into three identical pieces, and these pieces are stacked together so that like poles are aligned. What will be the new period of oscillation of this arrangement?

1. 2√(3) s
2. 2/3 s
3. 2 s
4. 2/√(3) s

Correct answer: 2 s

Solution

Each lengthwise strip has the same length, mass m/3 and moment M/3. Stacked with like poles aligned, total moment = M, total mass = m, total moment of inertia = m L^2/12 = original I. Since T = 2 pi sqrt(I/(M B)) is unchanged, the period stays 2 s.

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