A thin uniform rod of length 2 m, cross sectional area ' A ' and density ' d ' is rotated about an axis passing through the centre and perpendicular…

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