$[20]$ Particles each of mass $\backslash ($ m $\backslash )$ move out with negligible friction along the circular slots in the disk, which rotates in the horizontal plane with a constant angular velocity $\backslash (\backslash$omega $\backslash ).$ Derive an expression for the force $\backslash ($ F $\backslash )$ exerted by the slot on a particle in terms of $\backslash (\backslash$theta $\backslash ).$ Also determine the velocity $\backslash ($ u $\backslash )$ of the particle relative to the slot just prior to leaving the slot. Assume each particle starts essentially from rest at $\backslash (\backslash$theta $\backslash$cong $0\backslash ).$