Final answer:
The increase in length of the second wire with doubled dimensions and force will be the same as the first wire because the change in length is directly proportional to force and length, and inversely proportional to the cross-sectional area.
Step-by-step explanation:
The student's question pertains to the elasticity of wires, which is a topic in physics dealing with the deformation of materials under applied forces. Experiments show that the change in length (ΔL) of an object like a wire is proportional to the applied force (F), the original length (Lo), and inversely proportional to the cross-sectional area (A). The relation is represented by the equation:
ΔL = αFLo/A
where α is a proportionality constant known as the Young's modulus of the material.
To find the increase in length of the second wire, we must apply this principle considering that the second wire is twice as long and has a radius that is twice as large, thus having a cross-sectional area that is four times as large. The force applied is also doubled. Because the change in length is directly proportional to both the force and the original length but inversely proportional to the cross-sectional area, the increase in length of the second wire will be the same as that of the first wire, despite the differences in dimensions and applied force.