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  4. The time period of a thin bar magnet in earth's magnetic field is T. If the magnet is cut into four equal parts perpendicular to its length, the time period of each part in the same field will be

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Q. The time period of a thin bar magnet in earth's magnetic field is $T$. If the magnet is cut into four equal parts perpendicular to its length, the time period of each part in the same field will be

Magnetism and Matter

Solution:

Mass becomes $1 / 4$ and length becomes $1 / 4$.
$\therefore $ Moment of inertia $I$ becomes, $\frac{1}{4}\left(\frac{1}{4}\right)^{2}=\frac{1}{64}$ therefore Magnetic moment $M$ becomes $1 / 4$ th.
Now, as $T=2 \pi \sqrt{\frac{1}{M H}}$,
$\therefore T$ becomes $1 / 4$ th