With a standard rectangular bar magnet of length (l), breadth $(b;\ b

Question

With a standard rectangular bar magnet of length (l), breadth $(b;\ b < < l)$ and magnetic moment M, the time period of the magnet in vibration magnetometer is 4 s. If the magnet is cut normal to its length into four equal pieces, the time period (in second) with one of the pieces

Dr. Abubacker · Accepted Answer

(c) Time period of magnet in vibration magnetometer
$T = 2\pi\sqrt{\frac{I}{MB_{H}}}$
Where $I =$ moment of inertia of magnet,
$M =$ magnetic moment,
$B_{H} =$ horizontal component of earth’s magnetic field.
$	herefore\ \ \ \ \ \ \frac{T_{1}}{T_{2}} = \sqrt{\frac{I_{1}}{I_{2}}.\frac{M_{2}}{M_{1}}}$
$\ \ \ \ \ \ \ \ \ \frac{4}{T_{2}} = \sqrt{\frac{ml/12 	imes M/4}{m/4(l/4)^{2}/12 	imes M}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \  = \sqrt{\frac{4 	imes 16 	imes 12}{12 	imes 4}} = \sqrt{16}$
$\ \ \ \ \ \ \ \ \frac{4}{T_{2}} = 4$
$\Longrightarrow \ T_{2} = 1$s

Q. With a standard rectangular bar magnet of length (l), breadth $(b;\ b < < l)$ and magnetic moment M, the time period of the magnet in vibration magnetometer is 4 s. If the magnet is cut normal to its length into four equal pieces, the time period (in second) with one of the pieces

Explanation

Reviewed by Dr. Abubacker

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