A uniform rod $A B$ of length ' $L$ ' and mass ' $M$ ' is pivoted at the centre ' $O$ ' in such a way that it can rotate in the vertical plane as shown in the figure. An insect of the same mass falls vertically with speed ' $\mathrm{v}$ ' on the horizontal rod at a point ' $\mathrm{C}$ ' which is the midpoint of $\mathrm{O}$ and $\mathrm{B}$. Immediately after falling, the insect moves towards the end $B$ such that the rod rotates with constant angular velocity ' $\omega$ '. If the insect reaches the end B when the rod has turned through $90^{\circ}$, then the speed $v$ is