A) \[2s\]
B) \[2/3\text{ }s\]
C) \[2\sqrt{3}\text{ }s\]
D) \[2/\sqrt{3}\text{ }s\]
Correct Answer: B
Solution :
| [b] The time period of oscillations of magnet |
| \[T=2\pi \sqrt{\left( \frac{I}{MH} \right)}\] |
| where,\[l=\]moment of inertia of magnet\[=\frac{m{{L}^{2}}}{12}\] |
| (\[\because \]magnet can be consider as a thin rod of length L and m, being the mass of magnet) |
| \[M=pole\text{ }strength\times L\]and |
| H = horizontal component of the earth's magnetic field |
| When the three equal parts of magnet are placed on one another with their like poles together, then the new moment of inertia, |
| \[l'=\frac{1}{12}\left( \frac{m}{3} \right)\times {{\left( \frac{L}{3} \right)}^{2}}\times 3=\frac{1}{12}\frac{m{{L}^{{}}}}{9}=\frac{l}{9}\] |
| and the new magnetic moment, |
| \[M'=\]pole strength \[\times \frac{L}{3}\times 3=\]pole strength \[t\times L\]\[=M\] |
| Hence, \[T'=2\pi \sqrt{\left( \frac{l/9}{MH} \right)}\] |
| \[\Rightarrow \] \[T'=\frac{1}{3}\times T\] |
| \[T'=\frac{2}{3}s\] |
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