Final answer:
Gravitational torques depend on the mass of the objects, the distance from the pivot (lever arm), and gravity. Rod A, being twice as long, will have a larger lever arm, thus exhibiting a larger torque for the same mass distribution compared to shorter rods. Without details of each arrangement, we cannot rank the torques for A to D.
Step-by-step explanation:
Understanding Gravitational Torques
When dealing with gravitational torques around pivots, particularly in systems involving rods and weights, we look at the factors that influence torque magnitude. These include the mass of the objects, the distance from the pivot point (lever arm), and the gravitational force. Torque (τ) can be calculated using the equation τ = r × F × sin(θ), where r is the lever arm, F is the force, and θ is the angle between the force and the lever arm.
Given that rod A is twice as long as the others, it will have a larger lever arm for the same mass distributed at its end, thereby exerting a larger torque when compared to rods of shorter length with the same mass distribution. However, the exact ranking of the gravitational torques for the arrangements A to D cannot be defined without the explicit description of each arrangement and their respective lever arms and mass distributions.
It should also be noted that since we are considering gravitational torques, we assume that all masses involved are subjected to gravity, and thus, any mass not positioned at the pivot point will contribute to the net torque about that pivot.