Two similar beads each of mass m slide smoothly along a uniform rod mass M and length l. the rod can rotate along an axis passing through its centre and normal to its length. Initially, the rod is rotated with angular speed ${\mathrm{\omega }}_{\mathrm{i}}$ when beads are at the centre C of the rod. The angular speed ${\mathrm{\omega }}_{\mathrm{f}}$ of the rod when beads slide to the two ends of the rod without any external force is given by $\frac{{\mathrm{M\omega }}_{\mathrm{i}}}{(\mathrm{xm}+\mathrm{M})}$ where ‘x’ is ____