A rotating bar with a machined surface as shown in figure. The material is made from cold$-$drawn medium$-$carbon steel $($AISI $1040,$ quenched and tempered at $205^3*$ C $).$ The bar is subjected to force from F nes $=8,000$N to F$\_\{$m$\}=4000$N And steady axial force P $4000$ N$.$ Using the modified Goodman failure theory, determine the safety factors for the groove. d$\_\{2\}=25$mm $,$ D $=30$mm and d $=20$ mm$.$