b
The dipole experiences a torque \(pE\) \(\sin \theta\) tending to bring itself back in the direction of field.

Therefore, on being released (i.e. rotated) the dipole oscillates about an axis through its centre of mass and perpendicular to the field. If \(I\) is the moment of inertia of the dipole about the axis of rotation, then the equation of motion is

\(I\) \(\mathrm{d}^{2} \theta / \mathrm{dt}^{2}=-\mathrm{pE}\, \sin \theta\)

For small amplitude \(\sin \theta \approx \theta\)

Thus \(\mathrm{d}^{2} \theta / \mathrm{dt}^{2}=-(\mathrm{pE} / \mathrm{I}) \cdot \theta=-\omega^{2} \theta\)

where \(\omega=\sqrt{(\mathrm{pE} / \mathrm{I})}\)

This is a \(S.H.M.\), whose period of oscillation is

\(\mathrm{T}=2 \pi / \omega=2 \pi \sqrt{(\mathrm{I} / \mathrm{pE})}\)