Final answer:
Doubling the diameter of a wire increases the cross-sectional area fourfold and thus reduces stress for the same applied weight, leading to a lesser change in length than the original 16 cm stretch caused by a 5 kg weight.
Step-by-step explanation:
The question asks about the change in length of a wire under different conditions of weight and diameter, a scenario that involves principles of physics, particularly those related to elasticity and stress-strain relationships.
When the diameter of a wire is doubled, the cross-sectional area of the wire becomes four times larger because the area is proportional to the square of the diameter (Area ≈ π * (Diameter/2)2). Given that the original weight of 5 kg caused the wire to stretch by 16 cm, doubling the diameter would mean the cross-sectional area is now able to distribute the stress more effectively over a larger area, resulting in less strain for the same amount of stress (weight), assuming the material's Young's modulus remains constant.
Therefore, paradoxically, when the diameter is doubled, the increase in length will not double; in fact, the extension due to the same weight would be less than 16 cm because of the increased area, leading to a reduced stress per unit area. Among the options given (a, b, c, d), none directly correspond to the correct effect of doubling the diameter; however, the closest correct answer would be less than the original change in length (16 cm).