$11-27*$ The slender bar shown in Fig. P$11-27$ weighs $150$ lb $.$ If $\backslash (\backslash$mathbf$\{$P$\}=75\backslash$mathrm$\{$lb$\}\backslash )$ and $\backslash (\backslash$mathbf$\{$M$\}=50\backslash$mathrm$\{$ft$\}\backslash$cdot $\backslash$mathrm$\{$lb$\}\backslash ),$ determine the magnitude of the force F required to maintain the bar in the equilibrium position shown in the figure.

Fig. P$11-27.$ Must use method of virtual work!