Q. The period of oscillation of a freely suspended bar magnet is 4 s. If it is cut into two equal parts in length, then the time period of each part will be

A) 4 s
B) 2 s
C) 0.5 s
D) 0.25 s
Explanation

(b) From $T = 2\pi\sqrt{\frac{I}{MB}},4 = 2\pi\sqrt{\frac{I}{MB}}$.
When it is cut into two equal parts in length, mass of each part becomes $1/2$, $\ I = mass\ \frac{(length)^{2}}{12}$ becomes $\frac{1}{8}th$ and $M\ becomes\frac{1}{\ 2}.$
$T^{'} = 2\pi\sqrt{\frac{I/8}{(M/2)B}}$
$\therefore\ \ = \frac{1}{2}\left( 2\pi\sqrt{\frac{I}{MB}} \right)$
$= \frac{1}{2}T = 2$s

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.