Q. The length of magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is 2 s. The magnet is cut along its length into three equal parts and these parts are then placed on each other with their like poles together. The time period of this combination will be
A) $\frac{2}{\sqrt{3}}$s
B) $\frac{2}{3}\ $s
C) $2\sqrt{3}$s
D) 2 s
Explanation
(d) $T = 2s = 2\pi\sqrt{\frac{I}{MH}}.$
When the magnet is cut along its length into three equal parts, moment of inertia of each part becomes $I/3$ and magnetic moment of each part also becomes $M/3$.
As the three parts are placed on each other with their like poles together, therefore for the combination,
$T^{'} = 2\pi\sqrt{\frac{I/3 + I/3 + I/3}{(M/3 + M/3 + M/3)B}}$
$= 2\pi\sqrt{\frac{I}{MB}} = 2s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.