A dipole comprises of two charged particles of identical magnitude...

The data given is

$l =$distance between the charges

$q =$charge

$m =$mass of the positive charge

$2m$=mass of negative charge

The moment of inertia of the system is

$I = \left(\dfrac{m \times 2m}{m + 2m}\right){\left(l\right)}^{2} = \dfrac{2m{l}^{2}}{3}$

The angular frequency can be written as

$\omega = \sqrt{\dfrac{pE}{I}} . . . ( i )$

Substituting the value of moment of inertia in the equation (i) we get

$\omega = \sqrt{\dfrac{pE}{\dfrac{2m{l}^{2}}{3}}} = \sqrt{\dfrac{3pE}{2m{l}^{2}}}$

The value of the dipole moment is

$p = ql$

Hence, the angular frequency becomes

$\omega = \sqrt{\dfrac{3qE}{2ml}}$

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