Q12 / 49 · NTA Abhyas (JEE Main) 2020 · Physics · Magnetic Properties of Matter

A bar magnet has a magnetic moment equal to 5×10-5 Wb m. It is suspended in a magnetic field which has a magnetic induction B=8π×10−4 T. The magnet vibrates with a period of vibration equal to 15 s. The moment of inertia of magnet is

  • A
    4.54×104 kg m2
  • B
     4.54× 10 −5  kg m 2
  • C
     4.54× 10 −4  kg m 2
  • Correct answer
    D
     4.54× 10 5  kgm 2

Solution

Here, magnetic moment is given in weber-meter, which is the unit of μ0 M.

∴    μ0 M=5×10-5 Wb-m

           M=5×10-5μ0Am2

Also,    B=8π×10-4=μ0H

∴       H=8π×10-4μ0

          T=2πIMH

         I=MHT24π2=5×10-5×8π×10-4×1524π2μ02

           =5×10-5×8π×10-4×2254π24π×10-72

       I=2250×10-9π(16π2)×10-14=4.54×105 kg m2

Hence, the correct answer is option: 'D'.

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