A fixed$-$free bar has constant circular cross section of diameter $d=0\mathrm{.}01m$ and is externally loaded as shown in the Figure by axial forces where $P=2000$ N$.$ The bar material has the allowable stress ${}_a=420*{10}^6\frac{N}{m^2}.$

$($a$)$ Calculate the reaction at the fixed end $B.$

$($b$)$ Express and draw the diagram of the normal internal force N$.$

$($c$)$ Calculate the maximum normal stress ${}_{\text{m}\text{a}\text{x}}$ in the bar, and establish whether the bar is safe under the applied load.