The two spheres of equal mass m are able to slide along the horizontal rotating rod. If...

The two spheres of equal mass m are able to slide along the horizontal rotating rod. If they are initially latched in position a distance r from the rotating axis with the assembly rotating freely with an angular velocity ω₀, determine the new angular velocity ω after the spheres are released and finally assume positions at the ends of the rod at a radial distance of 2r. Also find the fraction n of the initial kinetic energy of the system which is lost. Neglect the small mass of the rod and shaft.