How many times is the relative elongation of a wire with a diameter d1 greater than a wire with a diameter d2 = 2d1

How many times is the relative elongation of a wire with a diameter d1 greater than a wire with a diameter d2 = 2d1, if the same forces are applied to the ends of the wire?

To calculate the ratio of the relative elongations of the wires taken, we use the formula: F / S = Ϭ = ε * E, whence we express: ε = F / (E * S).
The resulting equality: k = ε1 / ε2 = F / (E * S1) / F / (E * S2) = S2 / S1 = 0.25 * Π * d2 ^ 2 / (0.25 * Π * d1 ^ 2) = d2 ^ 2 / d1 ^ 2 = (d2 / d1) ^ 2.
Variable ratios: d2 (second wire diameter) = 2d1 (first wire diameter).
Let’s make the calculation: k = (d2 / d1) ^ 2 = (2d1 / d1) ^ 2 = 4 p.
Answer: The elongation of the first wire taken will be 4 times greater.