$.$ An aircraft link is made from an A$992$ steel circular rod $($E $=29,000[$ksi$]).$ The link is $48[$in$]$ long and supports a $2[$kip$]$ axial compressive load. The ends of are pin connected. Determine the smallest diameter of the rod, to the nearest $1/16$ that will support the load without buckling. Note that the second moment of area of a circular cross$-$section is I $=$ $/4*$R$4,$ where R is the radius of the cross$-$section. Determine the factor of safety against buckling with this diameter.