An electric dipole of dipole moment P is placed in a uniform electric field E is stable equilibrium position. Its moment of inertia about the centroidal axis is I. If it is displaced slightly from its mean position find the period of small oscillation.
Answer & explanation
Correct answer: option 2
When displaced at an angle θ, from its mean position the mean position the magnitude of restoring torque is
$\tau=-P E \theta$
For small angular displacement $\sin \theta \approx \theta$
$\tau=-PE \theta$
The angular acceleration is,
$\alpha=\frac{\tau \theta}{I}=-\left(\frac{pE}{I}\right) \theta=-\cos ^2 \theta$
Where $\omega^2=\frac{P E}{I}$
∴ $T=2 \pi \sqrt{\frac{I}{PE}}$