A thin uniform rod of length $2 \mathrm{~m}$, cross sectional area '$A$' and density '$\mathrm{d}$' is rotated about an axis passing through the centre and perpendicular to its length with angular velocity $\omega$. If value of $\omega$ in terms of its rotational kinetic energy $E$ is $\sqrt{\frac{\alpha E}{A d}}$ then value of $\alpha$ is ______________.