A) \[2s\]
B) \[2/3\text{ }s\]
C) \[2\sqrt{3}s\]
D) \[2/\sqrt{3}\text{ }s\]
Correct Answer: B
Solution :
The time period of oscillations of magnet \[T=2\pi \sqrt{\left( \frac{I}{MH} \right)}\] ?.(i) where\[I=\]moment of inertia of magnet \[=\frac{m{{L}^{2}}}{12}\] (m, being the mass of magnet) \[M=pole\text{ }strength\times L\] 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 \[I=\frac{1}{12}\left( \frac{m}{3} \right)\times {{\left( \frac{L}{3} \right)}^{2}}\times 3\] \[=\frac{1}{12}\frac{m{{L}^{2}}}{9}=\frac{I}{9}\] and \[M=\]pole strength \[\times \frac{L}{3}\times 3\] \[=M\] Hence, \[T=2\pi \sqrt{\left( \frac{I/9}{MH} \right)}\] \[\Rightarrow \] \[T=\frac{1}{3}\times T\] \[T=\frac{2}{3}s\]
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