Elasticity

The change in length of a wire due to an applied force is given by the formula: where is the applied force, is the length of the wire, is the cross-sectional area, and is the Young's modulus of the material.
Since both wires are made of the same material, is constant for both.
The cross-sectional area of a wire is proportional to the square of the radius:
Let the radius of the first wire be and the radius of the second wire be , with , so: Let the lengths of the wires be and , with . Now, using the formula for change in length: Substitute the ratios:
Thus, the ratio of their change in length is .