A dipole comprise 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 ‘ $\bar{E}$ ’, in such a way that dipole axis makes a very small angle with the electric field .’ $\bar{E}$ ’ .The angular frequency of the oscillations of the dipole when released is given by :

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$\sqrt{\frac{4 qE}{3 ml}}$

$\sqrt{\frac{4 qE}{ml}}$

$\sqrt{\frac{3 qE}{ml}}$

$\sqrt{\frac{8 qE}{3 ml}}$

answer is B.

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Detailed Solution

$\begin{array}{l} I = m {(\frac{L}{3})}^{2} + \frac{m}{2} \times {(\frac{2 L}{3})}^{2} \\ I = \frac{{mL}^{2}}{3} \\ q L E \sin θ = I α \\ q L E \sin θ = \frac{{mL}^{2}}{3} α \\ α = \frac{3 q E}{m L} θ \\ ω = \sqrt{\frac{3 q E}{m L}} \end{array}$