Final answer:
According to Hooke's law, the change in length of a material due to an applied force is dependent on the original force and the material's properties. For a wire under double the length, radius, and force, the increase in length will be the same as the original wire, which is 'x'. The correct answer is A. x.
Step-by-step explanation:
The student is asking about the effect of force on the elongation of wires which is a topic in physics, specifically related to Hooke's law and the physical properties of materials.
According to Hooke's law, the change in length (ΔL) of a wire due to a force (F) is proportional to the force applied and the original length (L0) of the wire, and inversely proportional to the cross-sectional area (A) of the wire. The equation for this is: ΔL = (F × L0) / (A × Y), where Y is Young's modulus for the material.
In the problem described, the changes in both wire length and radius should affect the change in length when a force is applied. For the first wire with length 'l' and radius 'r', the increase in length is 'x' when a force 'F' is applied. For the second wire, both the length and radius are doubled, and the force applied is also doubled. T
herefore, the second wire has four times the cross-sectional area (since cross-sectional area depends on the square of the radius), but we're applying twice the force on a wire that is twice as long. Thus, the increase in length for the second wire would mathematically also be 'x', showing an elasticty that doesn't change with the scale of the wire under the same material properties.
Therefore, the correct answer is A. x.