Question

With a standard rectangular bar magnet the time period of a vibration magnetometer is 4s. The bar magnet is cut parallel to its length into four equal pieces. The time period of vibration magnetometer when one piece is used (in second) (bar magnet breadth is small) is :

• A. 16
• B. 8
• C. 4
• D. 2

Answer 1

The correct option is C 4

Time period of vibration magnetometer is given as,

$T=2\pi \sqrt{I/mB}$,

When magnet is cut parallel to its length into four equal pieces. Then,now
Magnetic moment, $M^{\prime }=\frac{M}{4}$
New moment of inertia $I^{\prime }=\frac{I}{4}$
New time period $T^{\prime }=2\pi \sqrt{\frac{I^{\prime }}{M^{\prime }B}}$
$T^{\prime }=T^{\prime }=4s$