A plank is rotating in a vertical plane about one of its ends with a constant angular velocity $\omega =\sqrt{2}$ rad/s. A block of mass m = 2 kg is placed at a distance I = 1m from its end A (see diagram) which is hinged. The block starts sliding down when the plank makes an angle $\theta =30^{\circ }$ with the horizontal. If coefficient of friction between the plank and the block is $\mu$ and given that ${\mu }^2=\text{k/25}$. The value of k is