A uniform rod of length L rests on a frictionless horizontal surface. The rod is pivoted about a fixed frictionless axis at one and and is initially at rest. A bullet traveling parallel to the horizontal surface and perpendicular to the rod with speed V₀ strikes the rod at its centre and becomes embedded in it. The mass of the bullet is one-sixth of the mass of the rod. The final angular velocity of the rod is ($\mathrm{\omega }$)and the ratio of the kinetic energy of the system after collision to the kinetic energy of the bullet before collision is $\frac{1}{\mathrm{x}}$ where $\mathrm{x}$ is _________