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Question
A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their magnetic moment parallel to their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform magnetic field in such a manner that their magnetic moments make a small angle with the field. If the oscillation periods of hoop and cylinder are Th and Tc respectively, then:
Options
Th = Tc
Th = 2 Tc
Th = 1.5 Tc
Th = 0.5 Tc
MCQ
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Solution
Th = Tc
Explanation:
Using, time /oscillation period,
T = 2π `sqrt("I"/"MB")`
Where, M = magnetic moment, I moment of inertia and B = magnetic field
Th = 2π `sqrt("MR"^2/((2"MB")))`
Tc = 2π `sqrt((1//2"mR"^2)/"MB")`
Clearly, Th = Tc
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