A) \[\frac{2}{3}s\]
B) \[\sqrt{\frac{2}{3}}s\]
C) \[\frac{3}{2}s\]
D) \[\sqrt{\frac{3}{2}}s\]
Correct Answer: A
Solution :
The time period of oscillations of magnet \[T=2\pi \sqrt{\frac{I}{MH}}\] ... (i) where, \[I\]= moment of inertia of magnet \[=\frac{m{{l}^{2}}}{12}\] (m, being the mass of magnet) M = pole strength \[\times \,L\] and H = horizontal component of Earths magnetic field. When the three equal parts of magnet are placed on one another with their like poles together then \[I=\frac{1}{12}\left( \frac{m}{3} \right)\,{{\left( \frac{L}{3} \right)}^{2}}\times 3\] \[=\frac{1}{12}\frac{m{{L}^{2}}}{9}=\frac{I}{9}\] and M = Pole strength \[\times \frac{L}{3}\times 3=M\] Hence, \[T=2\pi \sqrt{\left( \sqrt{\frac{I/9}{MH}} \right)}\Rightarrow T=\frac{1}{3}\times T\] \[T=\frac{2}{3}s\]
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