Rotational Motion

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 ______________.