A small electric dipole \(\vec {p_0}\), having a moment of inertia I about its center, is kept at a distance r from the center of a spherical shell of radius R. The surface charge density \(\sigma\) is uniformly distributed on the spherical shell. The dipole is initially oriented at a small angle \(\theta\) as shown in the figure. While staying at a distance r, the dipole is free to rotate about its center.
![A small electric dipole](https://www.sarthaks.com/?qa=blob&qa_blobid=10066323198982990499)
If released from rest, then which of the following statement(s) is (are) correct?
[\(\varepsilon_0\) is the permittivity of free space.]
(A) The dipole will undergo small oscillations at any finite value of r.
(B) The dipole will undergo small oscillations at any finite value of r > R.
(C) The dipole will undergo small oscillations with an angular frequency of \(\sqrt{\frac{2\sigma p_0}{\varepsilon_0I}}\) at \(r = 2R\)
(D) The dipole will undergo small oscillations with an angular frequency of \(\sqrt{\frac{\sigma p_0}{100\varepsilon_0I}}\) at \(r =10R\)