Oscillations

JEE Main level, single correct, medium

134 of 194

Question 134 of 194

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 Th{T}_{h} and Tc{T}_{c} respectively, then:

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Answer: (B) Th=Tc{T}_{h}={T}_{c}

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

T=2πIMBT=2\pi \sqrt{\dfrac{I}{MB}}

Thoop=2πmR2MB{T}_{hoop}=2\pi \sqrt{\dfrac{m{R}^{2}}{MB}} ...... (1)(1) Ihoop=mR2{I}_{hoop}=m{R}^{2}

Tc=2πmR22M2(B){T}_{c}=2\pi \sqrt{\dfrac{\dfrac{m{R}^{2}}{2}}{\dfrac{M}{2}\left(B\right)}} ...... (2)(2) ISolidcylinder=mR22{I}_{Solidcylinder}=\dfrac{m{R}^{2}}{2}

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

Th=Tc{T}_{h}={T}_{c}

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