I know the answer is the last option with the X beside it, I just don\'t underst

Question

I know the answer is the last option with the X beside it, I just don't understand how the answer is found or what equations are used. Thanks!

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A magnetic dipole with dipole moment of magnitude is immersed in a uniform magnetic field of magnitude B as shown in the figure to right above. The mass of the dipole is m. The moment of inertia of the dipole around an axis through its center perpendicular to the page is I. The dipole

[A] accelerates along the magnetic field with acceleration (B) / m

[B] performs simple harmonic motion around the direction of B with frequency = I / (B)

[C] performs simple harmonic motion around the direction of B with frequency = sqrt[ I / (B) ]

[D] performs simple harmonic motion around the direction of B with frequency = (B) / I

[X] performs simple harmonic motion around the direction of B with frequency = sqrt[ (B) / I ]

Explanation / Answer

Torque on the magnetic dipole = u X B = uB sin theta

for small theta torque = uB theta

i*alpha = uB theta,

alpha = [uB/i] theta

Angular acceleration is proportional to theta, so it will perform SHM

comparing with alpha = w^2 theta,

so w^2 = uB/i,

w = sqrt(uB/i)

so last option is correct.

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