A small electric dipole $\vec{p}_0$, having a moment of inertia / 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.
Select ALL correct options:
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 $\sqrt{\frac{2 \sigma p_0}{\varepsilon_0 I}}$ at $r=2 R$
D
The dipole will undergo small oscillations with an angular frequency of $\sqrt{\frac{\sigma p_0}{100 \varepsilon_0 l}}$ at $r=10 R$
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