JEE Main · 2004 · 24 Apr 2004 · Offline · Magnetic Properties of Matter

In a vibration magnetometer the period is $T=2\pi \sqrt{\frac{I}{MB}}$. Cutting the magnet into three equal pieces and stacking them makes the moment of inertia $\frac{I}{9}$, while the magnetic moment is unchanged, since each piece keeps one-third of the length but there are three of them. The period therefore scales as $\sqrt{\frac{1}{9}}=\frac{1}{3}$, so it falls to a third of its value, $\frac{2}{3}$ s.