$3.$ A block of mass $\backslash (\backslash$mathbf$\{$M$\}\backslash )$ hangs from a uniform, rigid rod of mass $\backslash (\backslash$mathbf$\{$m$\}\backslash )$ and length $\backslash (\backslash$mathbf$\{$L$\}\backslash )$ as shown on the diagram. The other end of the rod is attached to the wall through a frictionless hinge. The rod is also supported by a massless, inelastic metal cable, connected to the rod at a distance $\backslash (\backslash$mathbf$\{$d$\}\backslash )$ away from the hinge.

Given variables: $\backslash (\backslash$mathbf$\{$M$\},\backslash$mathbf$\{$m$\},\backslash$mathbf$\{$L$\},\backslash$mathbf$\{$d$\},\backslash$boldsymbol$\{\backslash$theta$\},\backslash$boldsymbol$\{\backslash$varphi$\}\backslash )$

a$)$ Draw a free$-$body diagram for the beam. $(4$ points$)$

b$)$ Find the tension on the metal cable. $(4$ points$)$

c$)$ Find the horizontal and vertical components of the force at the hinge. $(6$ points$)$