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A bar magnet is oscillating in Earth's magnetic field with periodic time T. If a similar magnet with same mass and volume has magnetic dipole moment, which is 9 times that of this magnet, then the periodic time will be ______.

Asked in GUJCET 2013 · Dipole in a uniform field

Answer: (3) T/3

Step-by-step solution

Given: same mass and same volume, so the same shape and the same moment of inertia I; the magnetic moment goes from m to 9m; the place is the same, so the horizontal field B_H is unchanged.

Idea: a magnet swinging in a horizontal field is an angular simple harmonic oscillator, with T=2π√I/(mB_H).

Only m changes here, so T∝1/(√m).

(T')/T=√m/(9m)=1/3.

So T'=T/3: a nine-fold stronger magnet swings three times faster, not nine times faster.

Why the other options are wrong

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