Two wires of the same material and same length but diameters in the ratio 1: 2 are stretched by the same force. The potential energy per unit volume of the two wires will be in the ratio

it is given that, both wires are made by same material, length of wires are same and also same force applied to the end of wire . hence, strain of both wires will be same.

Strain = stress/Y

where Y is Young’s modulus.

so, potential energy per unit volume = 1/2 × (stress)²/Y

but we know, stress is inversely proportional to square of diameter of wire.

so, potential energy per unit volume is inversely proportional to (diameter)⁴.

so, ratio of potential energy per unit volume = (d2/d1)⁴

Given that d1 : d2 = 1:2

so, ratio of potential energy per unit volume = 2⁴/1⁴ = 16/1