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 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. $2s$

Answer 1

Answer: (B)

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