A bar magnet makes 40 oscillations per minute in a vibration magnetometer. An identical magnet is demagnetised…

Q: A bar magnet makes 40 oscillations per minute in a vibration magnetometer. An identical magnet is demagnetised completely and is placed over the magnet in the magnetometer. Calculate the time taken for 40 oscillations by this combination. Ignore induced magnetism.

Sol. In this first case, frequency of oscillation,

$\large \nu = \frac{1}{2\pi} \sqrt{\frac{M B}{I}}$

In the second case, frequency of oscillation,

$\large \nu’ = \frac{1}{2\pi} \sqrt{\frac{M B}{2 I}}$

$\large \frac{\nu’}{\nu} = \frac{1}{\sqrt{2}}$

$\large \frac{T’}{T} = \sqrt{2} $

$\large T’ = \sqrt{2} T $

Now , $\large 40 T’ = \sqrt{2} T \times 40 $