A) is proportional to E
B) is proportional to 1/E
C) is \[\pi \sqrt{\frac{m\ell }{3qE}}\]
D) is proportional to \[\frac{1}{\sqrt{E}}\] but \[\ne \pi \sqrt{\frac{m\ell }{3qE}}\]
Correct Answer: C
Solution :
\[I=\frac{m{{\ell }^{2}}}{12};\] Restoring troque \[=qE\ell \sin \theta \approx qE\ell \theta =\frac{{{d}^{2}}\theta }{d{{t}^{2}}}\] \[\therefore \] \[\omega =\sqrt{\frac{qE\ell }{I}}=\sqrt{\frac{qE\ell \times 12}{m{{\ell }^{2}}}}=\frac{2\pi }{T}\] \[\therefore \] \[T=\pi \sqrt{\frac{m\ell }{3qE}}\]
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