$2-(10$ pts$)$ A rotating round machine component, made of steel, is subjected to a bending moment that varies between $100in-1b$ to $300in-lb.$ The fatigue stress concentration factor, at the critical location, is estimated to be $K_f=1\mathrm{.}5.$ The component has a machined surface finish and is made of steel with $S_{ut}=120$ kpsi $.$ It is desired to have an infinite life and a reliability of $99\%.$ For a safty factor of $1\mathrm{.}5,$ determine the diameter of the bar. Use modified Goddman diagram and assume $K_{fm}=1\mathrm{.}0.$ Hint: assume size factor, check safety factor and readjust the diafneter.