The correct answer is D) the davit arm to pivot on the traveling nut and the head to fall outboard. Explanation: The quadrantal davit uses a worm gear and quadrant mechanism to control the lowering and raising of a boat. If the quadrant experiences excessive wear or tooth failure, it will cause the mechanism to become unstable. This will allow the davit arm to pivot freely on the traveling nut, causing the davit head to fall outboard in an uncontrolled manner. This is the expected outcome when the quadrant mechanism fails, as it removes the structural integrity needed to safely lower the boat. The other answer choices are incorrect because they do not accurately describe the likely outcome of quadrant failure. The limit switch, traveling nut, and winch brake are not directly affected by quadrant failure in this scenario.