A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in

Question

A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with 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 T h and T c respectively, then:

TestHub · Accepted Answer

Time period of any magnetic body place in an external magnetic field is:-

$T = 2 π \sqrt{\frac{I}{M B}}$

$T_{h o o p} = 2 π \sqrt{\frac{m R^{2}}{M B}}$ ...... $(1)$ $I_{h o o p} = m R^{2}$

$T_{c} = 2 π \sqrt{\frac{\frac{m R^{2}}{2}}{\frac{M}{2} (B)}}$ ...... $(2)$ $I_{S o l i d c y l i n d e r} = \frac{m R^{2}}{2}$

From $(1)$ and $(2)$

$T_{h} = T_{c}$

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