$5.$ A cold$-$drawn AISI$-1050$ steel torsion bar $\backslash ($ C B $\backslash )$ of diameter $\backslash ($ d $\backslash )$ is fastened to a rigid arm at $\backslash ($ A $\backslash ),$ supported by a bearing at $\backslash ($ C $\backslash ),$ and fixed at $\backslash ($ B $\backslash ),$ as depicted in the figure below. At the right end of the arm, the tire wheel is mounted on which the vertical force $\backslash ($ P $\backslash )$ acts from the ground. If the load $\backslash (\backslash$mathrm$\{$P$\}=500\backslash$mathrm$\{$~N$\}\backslash ),$ and a factor of safety is $1\mathrm{.}5$ determine the diameter d of the bar.