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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Magnetic Properties of Matter

NTA Abhyas 2020 · Physics · Magnetic Properties of Matter

A hoop and a solid cylinder of same mass and radius are made of a...

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:

Options

  1. ATh=2Tc{T}_{h} = 2{T}_{c}
  2. BTh=Tc{T}_{h} = {T}_{c}
  3. CTh=0.5Tc{T}_{h} = 0.5{T}_{c}
  4. DTh=1.5Tc{T}_{h} = 1.5{T}_{c}

Correct answer

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

Step-by-step solution

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{mR^{2}}{MB}}...... (1)Ihoop=mR2( 1 ){I}_{hoop} = mR^{2}

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

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

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