Time period of oscillations with a standard rectangular bar magnet the time period of a vibration magnetometer is 4 seconds. The bar magnet is cut parallel to its length into four equal pieces. The time period is, when one piece is used (in seconds) …………

$T=2\pi \sqrt{\frac{I}{M{B}_H}}=4\sec \mathrm{...........}\left(1\right)$

$$\begin{gathered} When bar magnet is cut in 4 parts along length, \\ its pole strength and mass becomes {\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.\right)}^{th} but length remains same. \end{gathered}$$

$Moment of Inertia = \frac{mass\times lengt{h}^2}{12}$

$\therefore I\text{'} = \frac{I}{4}$

$$\begin{gathered} Magnetic Moment = pole strength \times length \\ \therefore M\text{'} = \frac{M}{4} \end{gathered}$$

$$\begin{gathered} New Time Period will be, \\ {T}^1=2\pi \sqrt{\frac{\frac{I}{4}}{\frac{M}{4}{B}_H}}=2\pi \sqrt{\frac{I}{M{B}_H}} = 4 sec [from equation (1\left)\right] \end{gathered}$$