Final answer:
When a wire is stretched to four times its original length, its radius becomes half of the original radius to keep the volume constant. Therefore, the new radius is A. r/2.
Step-by-step explanation:
When a wire is stretched to four times its original length, the volume of the wire remains constant because the material of the wire does not change. As a result, the cross-sectional area of the wire changes to accommodate the change in length.
Given that the volume (V) is the product of the cross-sectional area (A) and length (L), and the volume stays constant, we can write V = A1 x L1 = A2 x L2, where the subscripts 1 and 2 refer to the original and stretched states, respectively.
If the original length is L and the original radius is r, then the original volume is πr2L. When stretched, the length becomes 4L and if we call the new radius r', the new volume is πr'24L.
Setting the two volumes equal to each other and solving for r' gives us r' = r/2, so the correct answer is (A) r/2.