The density of a rod gradually decreases from one end to the other. It is pivoted at one end such that it can move about a vertical axis passing through the pivot. A horizontal force F is exerted on the free end in a direction perpendicular to the rod. Which of the following quantities does not depend on which end of the rod is pivoted?

Step-by-step solution

Let the length of the rod be L . When the rod is pivoted at one end and a horizontal force F is applied at the free end perpendicular to the rod, the torque about the pivot is given by = F L . This torque depends only on the magnitude of the force and the length of the rod. It is independent of the mass distribution or which end is chosen as the pivot. The moment of inertia I of the rod depends on the mass distribution. Since the density gradually decreases from one end to the other, the moment of inertia about the