Probability — practice question

A uniform rod $AB$ weighs $6\,\text{N}$ and measures $0.8\,\text{m}$ in length. It is in limiting equilibrium with $B$ touching a rough horizontal plane, and $AB$ is at an angle of $60^\circ$ to the horizontal. A force keeps the rod in equilibrium in the vertical plane containing $AB$; it acts at $A$ and makes an angle of $45^\circ$ with $AB$ (see diagram).