A) \[\sqrt{2}s\]
B) \[2s\]
C) \[\frac{1}{\sqrt{2}}s\]
D) \[\frac{1}{2}s\]
Correct Answer: A
Solution :
Key Idea: Motion of magnet is SHM. When I is moment of inertia of magnet about its axis of vibration and H is horizontal component of earths magnetic field, then time period of magnet is \[T=2\,\pi \sqrt{\frac{I}{MH}}\] where M is magnetic moment. Given, \[n=30\] oscillation/min. Since, \[n=\frac{1}{T}\] \[\Rightarrow \] \[{{T}_{1}}=\frac{60}{30}s=2\,s\] Given, \[{{H}_{1}}=H,\,{{H}_{2}}=2H\] \[\therefore \] \[\frac{{{T}_{1}}}{{{T}_{2}}}=\sqrt{\frac{{{H}_{2}}}{{{H}_{1}}}}\] \[\frac{{{2}^{2}}}{T_{2}^{2}}=2\] \[\Rightarrow \] \[{{T}_{2}}^{2}=2\,s\] \[\Rightarrow \] \[{{T}_{2}}=\sqrt{2}\,s\]
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