The time period of a vibration magnetometer i | vedclass

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(A) The time period of a vibration magnetometer is given by the formula: $T = 2\pi \sqrt{\frac{I}{MB_H}}$,where $I$ is the moment of inertia,$M$ is th

Vedclass · Accepted Answer

$3T_0$

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(A) The time period of a vibration magnetometer is given by the formula: $T = 2\pi \sqrt{\frac{I}{MB_H}}$,where $I$ is the moment of inertia,$M$ is the magnetic moment,and $B_H$ is the horizontal component of the Earth's magnetic field.Given that the new magnet has a moment of inertia $I' = 3I$ and a magnetic moment $M' = M/3$.The new time period $T'$ is given by: $T' = 2\pi \sqrt{\frac{I'}{M'B_H}}$.Substituting the values: $T' = 2\pi \sqrt{\frac{3I}{(M/3)B_H}} = 2\pi \sqrt{9 \cdot \frac{I}{MB_H}} = 3 \cdot 2\pi \sqrt{\frac{I}{MB_H}}$.Therefore,$T' = 3T_0$.

The time period of a vibration magnetometer is $T_0$. Its magnet is replaced by another magnet whose moment of inertia is $3$ times and magnetic moment is $1/3$ of the initial magnet. The new time period will be:

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