Final answer:
A second steel wire, identical in material but with half the radius of the first, can support one fourth of the load W before reaching its elastic limit, which is W/4. The correct answer is option c) W/4.
Step-by-step explanation:
The student asks how much load a steel wire with half the radius of another wire, made of identical steel, can support before reaching its elastic limit.
The tensile strength of a wire (which determines the maximum load before reaching the elastic limit) is directly proportional to the cross-sectional area of the wire.
The cross-sectional area of a wire is proportional to the square of the radius (r^2).
Therefore, if the second wire has half the radius of the first wire, its radius is (1/2)r, and its cross-sectional area will be (1/2)^2 times that of the first wire, which is 1/4th.
Hence, the second wire can support a maximum load of W/4 before reaching its elastic limit.