Question

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

• A. $2s$
• B. $2/3s$
• C. $2\surd 3s$
• D. $2/\surd 3s$

Answer 1

Answer: (B)

$2/3s$

initially the time period of the magnet
$T=2=2\pi \sqrt{\frac{I}{MB}}......\left(i\right)$
For each part , its moment of inertia $=\frac{I}{27}$ and magnetic moment $=\frac{M}{3}$
$\therefore$ moment of inertia of system $I_s=\frac{I}{27}\times 3=\frac{I}{9}$
Magnetic moment of system $M_s=\frac{M}{3}\times =M$
Time period of system
$T_s=2\pi \sqrt{\frac{I_s}{M_{s}B}}=\frac{1}{3}\times 2\pi \sqrt{\frac{I}{MB}}=\frac{T}{3}=\frac{2}{3}sec$