$\sqrt[\phantom{2}]{?}4.(25\%)$ A uniform rod of weight $mg$ and length $L$ is supported at $30$ from the horizontal position by a pin connection at point A and a wire of negligible mass at point $B$ as shown in the right, $($the mass moment of inertia about its center of gravity is $m\frac{L^2}{12}$ and about point A is $($:$m\frac{L^2}{3}$