Physics Question from JEE Main 2023 · 30 January, Shift 1

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

$$\omega = \sqrt{\frac{\alpha E}{Ad}}$$

then the value of $\alpha$ is _____.