The strength of the magnetic field in which t | vedclass

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Question

(A) The frequency of oscillation $
u$ of a vibration magnetometer is given by the formula $
u = \frac{1}{2\pi} \sqrt{\frac{MB}{I}}$,where $M$ is the

Vedclass · Accepted Answer

Twice its original value

Vedclass · Answer

(A) The frequency of oscillation $
u$ of a vibration magnetometer is given by the formula $
u = \frac{1}{2\pi} \sqrt{\frac{MB}{I}}$,where $M$ is the magnetic moment,$B$ is the magnetic field strength,and $I$ is the moment of inertia.From this relation,we can see that $
u \propto \sqrt{B}$.Let the initial frequency be $
u_1$ and the initial magnetic field be $B_1$. Let the final frequency be $
u_2$ and the final magnetic field be $B_2 = 4B_1$.Then,$\frac{
u_2}{
u_1} = \sqrt{\frac{B_2}{B_1}} = \sqrt{\frac{4B_1}{B_1}} = \sqrt{4} = 2$.Therefore,$
u_2 = 2
u_1$.The frequency becomes twice its original value.

The strength of the magnetic field in which the magnet of a vibration magnetometer is oscillating is increased $4$ times its original value. The frequency of oscillation would then become

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