Final answer:
The stiffness of cylindrical objects like a half pin and carbon fiber bar is proportional to their individual radii to the fourth power.
Step-by-step explanation:
The stiffness of materials like a half pin and carbon fiber bar is usually expressed in terms of their geometrical and material properties. In the context of cylindrical objects like pins and bars, stiffness can be related to the moment of inertia, which itself is proportional to the fourth power of the radius for a solid cylinder. Therefore, the stiffness of a half pin and a carbon fiber bar, when treated as cylindrical objects, would be proportional to their individual radii to the fourth power.
It's important to note that this is a simplification and actual stiffness can be affected by factors such as the material's modulus of elasticity, the shape of the cross-section, and whether the material is solid or hollow. However, for the purposes of this explanation, the key relationship between radius and stiffness for a solid cylindrical rod is to the fourth power.