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 period of hoop and cylinder are Th and Tc respectively, then

Engineering

Physics

Magnetic Field

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 period of hoop and cylinder are T_h and T_c respectively, then

T_h = T_c

T_h = 1.5 T_c

T_h = 2T_c

T_h = 0.5T_c

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$∵ T = 2 π \sqrt{\frac{I}{μB}}$

$\frac{T_{h}}{T_{c}} = \sqrt{\frac{I_{R}}{I_{c}} \times \frac{μ_{c}}{μ_{h}}}$

$= \sqrt{2 \times \frac{1}{2}} = 1$

T_h = T_c