Question & Answer » Physics Questions » Two wires of the same Material and same length but diameters in the ratio 1: 2 are stretched by the same force. The two wires’ potential energy per unit volume will be in the ratio.

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

Answer: Both the wires are made up of the same material, the length of the wires is the same, and the same force is applied to the end of the wire. Therefore, the strain applied to both wires will be the same. Strain = stress/Y. Here, Y is Young’s modulus. The formula for potential energy per unit volume = 1/2 × (stress)²/Y Stress is inversely proportional to (diameter of wire)2. Potential energy per unit volume is inversely proportional to (diameter)⁴. The formula for ratio of potential energy per unit volume = (d2/d1)4 Given that d1 : d2 = 1:2 Therefore, the ratio of potential energy per unit volume = 2⁴/1⁴ = 16/1.