$6/195$ The slotted circular disk whose mass is $6$ kg has a radius of gyration about $\backslash ($ O $\backslash )$ of $175$ mm $.$ The disk carries the four steel balls, each of mass $0\mathrm{.}15$ kg and located as shown, and rotates freely about a vertical axis through $\backslash ($ O $\backslash )$ with an angular speed of $120\backslash (\backslash$mathrm$\{$rev$\}/\backslash$mathrm$\{$min$\}\backslash ).$ Each of the small balls is held in place by a latching device not shown. If the balls are released while the disk is rotating and come to rest relative to the disk at the outer ends of the slots, compute the new angular velocity $\backslash (\backslash$omega $\backslash )$ of the disk. Also find the magnitude $\backslash (|\backslash$Delta E$|\backslash )$ of the energy loss due to the impact of the balls with the ends of the slots. Neglect the diameter of the balls and discuss this approximation.