R$184.$ The spool has a mass of $60$ kg and a radius of

gyration of k G $=0\mathrm{.}3$ m$.$ If it is released from rest, determine

how far its center descends down the smooth plane before it

attains an angular velocity of v $=6$ rad$>$s$.$ Neglect the mass

of the cord which is wound around the central core. The

coefficient of kinetic friction between the spool and plane

at A is mk $=0\mathrm{.}2$