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A magnet freely suspended in a vibrational magnetometer makes 10 oscillations per minute at a place A and 40 oscillations per minute at a place B. If Earth's magnetic field at A is 36 \times 10^{-6} T. Value of B is 

  • Option 1)

    36\times 10^{-6} T

  • Option 2)

    72\times 10^{-6} T

  • Option 3)

    144\times 10^{-6} T

  • Option 4)

    0 T

 

Answers (1)

\\* T = 2\pi\sqrt{\frac{I}{mB}} \Rightarrow T\;\alpha\;\frac{1}{\sqrt{B}} \\* \frac{T_{A}}{T_{B}} = \sqrt{\frac{B_{B}}{B_{A}}} \Rightarrow \frac{^{60}/_{10}}{^{60}/_{20}} = \sqrt{\frac{B_{B}}{36\times10^{-6}}} \\* \Rightarrow B_{B} = 144\times10^{-6}

 

SHM of Bar Magnet in a Magnetic Field -

T = 2\pi \sqrt{\frac{I}{MB}}

I \rightarrow Moment of Inertia of magnet

M \rightarrow Magnetic moment of magnet

B \rightarrow Magnetic field

- wherein

* In uniform Magnetic field Bar magnets performs SHM.

* Formula

 

 


Option 1)

36\times 10^{-6} T

This is incorrect.

Option 2)

72\times 10^{-6} T

This is incorrect.

Option 3)

144\times 10^{-6} T

This is correct.

Option 4)

0 T

This is incorrect.

Posted by

Vakul

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