Question

With a standard rectangular bar magnet, the time period in a vibration magneto meter is $4sec.$ The bar magnet is cut parallel to its length into $4$ equal pieces. The time period in vibration magnetometer when the piece is used $($in sec$\left)\right($bar magnet breadth is small$)$

• A. $16$
• B. $8$
• C. $4$
• D. $2$

Answer 1

The correct option is C $4$

Time period of vibration: $T\propto \sqrt{\frac{I}{M}}$ where $I$ is the moment of inertia and $M$ is the magnetic moment
$\therefore$ $\frac{T_1}{T_2}=\sqrt{\frac{I_1{M}_2}{I_2{M}_1}}$
When the magnet is cut into 4 pieces parallel to its length, magnetic moment remains same since the breadth is very small..
$\therefore M_1=M_2$
Moment of inertial also does not change.
$I_2=I_1$
$\therefore \frac{T_1}{T_2}=\sqrt{\frac{I_1{M}_2}{I_2\times M_1}}=1$
$\therefore T_2=T_1=4$