A fixed$-$free bar has constant square cross section of side length $h=0\mathrm{.}015m$ and is externally loaded as shown in the Figure by axial forces where P is unknown. The bar material has the allowable stress ${}_a=400*{10}^6\frac{N}{m^2}.$

$($a$)$ Calculate the reaction at the fixed end $B$ in terms of $P.$

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

$($c$)$ Calculate the value of P that can safely be applied to the bar.