A dipole comprises of two charged particles of identical magnitude $q$ and opposite in nature. The mass $m$ of the positive charged particle is half of the mass of the negative charged particle. The two charges are separated by a distance $l$. If the dipole is placed in a uniform electric field $\vec E$ in such a way that dipole axis makes a very small angle with the electric field $\vec E$, the angular frequency of the oscillations of the dipole when released is given by
Answer: (A) $\sqrt{\dfrac{3qE}{2ml}}$
The dipole rotates about its centre of mass, which is $\dfrac{2l}{3}$ from $m$ and $\dfrac l3$ from $2m$:
$$I=m\left(\frac{2l}{3}\right)^2+2m\left(\frac l3\right)^2=\frac23ml^2$$
Restoring torque $\tau=qEl\sin\theta\approx qEl\theta$, so $\omega=\sqrt{\dfrac{qEl}{\frac23ml^2}}=\sqrt{\dfrac{3qE}{2ml}}$.
Solution by Sreeraj P, M.Sc Physics