A uniform beam of length $$L$$ and mass $$m$$ shown in figure $$P12.16$$ is inclined at an angle $$\theta $$ to the horizontal. Its upper end is connected to a wall by a rope, and its lower end rests on a rough, horizontal surface. The coefficient of static friction between the beam and surface is $$\mu_s$$, Assume the angle $$\theta $$ is such that the static friction force is at its maximum value.
Using the condition of rotational equilibrium, find an expression for the tension $$T$$ in the rope in terms of $$m,g$$ and $$\theta$$.