With a standard rectangular bar magnet the time period of a vibration magnetometer is 4 s. 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

Question

Dr. Abubacker · Accepted Answer

(c) Time period of magnet, $T = 2\pi\sqrt{\frac{I}{MB_{H}}}$
When magnet is cut parallel to its length into four equal pieces. Then new magnet moment, $M’\  = \frac{M}{4}$
New moment of inertia, $I^{'} = \frac{I}{4}$
$	herefore$ New time period, $T’ = 2\pi\sqrt{\frac{I^{'}}{M^{'}B_{H}}}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ T = T^{'} = 4s$

Q. With a standard rectangular bar magnet the time period of a vibration magnetometer is 4 s. 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

Explanation

Reviewed by Dr. Abubacker

Want more practice?