Physics
Physics
Problem
Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is , the ratio of their diameters is: a. b. c. d.Intuitive explanation
The key is connecting elastic energy density to the material's stress and strain. Since both wires carry the same load and have the same length, they experience identical stress. Energy density depends on stress squared divided by the elastic modulus—but here's the insight: for the same material (steel) under the same stress, the wire storing less energy per unit volume must be thicker, because a thicker wire distributes that stress over more material. Use the relationship between energy density, stress, and Young's modulus to find how diameter scales with the energy ratio.
Intuitive explanation
The key is connecting elastic energy density to the material's stress and strain. Since both wires carry the same load and have the same length, they experience identical stress. Energy density depends on stress squared divided by the elastic modulus—but here's the insight: for the same material (steel) under the same stress, the wire storing less energy per unit volume must be thicker, because a thicker wire distributes that stress over more material. Use the relationship between energy density, stress, and Young's modulus to find how diameter scales with the energy ratio.