Question

The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is 2s. The magnet is cut along its length into three equal parts and then placed on each other with their like poles together. The time period of oscillations for this combination will be :

• A. $\frac{2}{\sqrt{3}}s$
• B. $\frac{2}{3}s$
• C. $2\sqrt{3}s$
• D. $2s$

Answer 1

Answer: (B)

$\frac{2}{3}s$

$T=2\pi \sqrt{\frac{I}{MB}}=2$
Moment of inertia of each part $\frac{I}{27}$ and magnetic moment $=\frac{M}{3}$
$\therefore$ New M.I $I^{\prime }=3\frac{I}{27}=\frac{I}{9}$
New magnetic moment $M^{\prime }=3\frac{M}{3}=M$
$T^{\prime }=2\pi \sqrt{\frac{I/9}{MB}}=\frac{1}{3}2\pi \sqrt{\frac{I}{MB}}=\frac{2}{3}s$