A hollow straight tube of length L and mass m can turn freely about its centre normal to its length on a smooth horizontal table. Another smooth uniform rod of same length and mass is fitted into the tube so that their centers coincide. The system is set in motion with an initial angular velocity ${\omega }_0^{ }$. The angular velocity of the rod at an instant when the rod slips out of the tube is  ${\omega }_0^{ }/k$. Find the value of $k$