The length of a magnet is large compared to its width and breadth… | JEE Main 2004 (AIEEE)

Q16JEE Main 2004 · AIEEEDifficult

Vibration Magnetometer

The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is $2\text{ s.}$ The magnet is cut along its length into three equal parts and these parts are then placed on each other with their like poles together. The time period of this combination will be

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Answer: (b)

Taking the three pieces as each of length $\dfrac{l}{3}$ : mass $\dfrac{m}{3}$ , moment $\dfrac{M}{3}$ , and $I_1 = \dfrac{(m/3)(l/3)^2}{12} = \dfrac{I}{27}$ .
Stacked with like poles together: $I' = 3\cdot\dfrac{I}{27} = \dfrac{I}{9}$ , $M' = 3\cdot\dfrac{M}{3} = M$ .
$T' = 2\pi\sqrt{\dfrac{I'}{M'B_H}} = \dfrac{T}{3} = \dfrac{2}{3}\ \text{s}$
So the answer is (b) $\dfrac{2}{3}$ s.

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Vibration Magnetometer question from JEE Main 2004 (AIEEE)

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