Final answer:
Two wires of the same length and material, but with diameters in a ratio of 1:2, will have the same potential energy per unit volume when stretched, leading to a ratio of 1:1 for potential energy per unit volume.
Step-by-step explanation:
The question pertains to the potential energy per unit volume when two wires with the same length and material but different diameters are stretched.
If the diameters are in a ratio of 1:2 and they are stretched by the same potential energy per unit volume, we need to consider how potential energy and volume change with diameter.
Because both wires are made of the same material and have the same length, and the potential energy per unit volume is constant for both, the potential energy for the two wires will remain the same when stretched by the same amount.
The ratio of potential energy per unit volume for the two wires remains 1:1, irrespective of their diameter difference.