A) \[{{\left( \frac{pE}{l} \right)}^{1/2}}\]
B) \[{{\left( \frac{pE}{l} \right)}^{3/2}}\]
C) \[{{\left( \frac{l}{pE} \right)}^{1/2}}\]
D) \[{{\left( \frac{p}{lE} \right)}^{1/2}}\]
Correct Answer: A
Solution :
[a] When dipole is given a small angular displacement \[\theta \]about its equilibrium position, the restoring torque will be \[\tau =-pE\sin \theta =-pE\theta (assin\theta =\theta )\] or \[I\frac{{{d}^{2}}\theta }{d{{t}^{2}}}=-pE\theta (as\,\tau =I\alpha =I\frac{{{d}^{2}}\theta }{d{{t}^{2}}})\] or \[\frac{{{d}^{2}}\theta }{d{{t}^{2}}}=-{{\omega }^{2}}\theta \,\,\text{with}\,\,{{\omega }^{2}}=\frac{pE}{I}\Rightarrow \omega =\sqrt{\frac{pE}{I}}\]
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