Elastic Potential Energy in a Stretched Wire

When an elastic material with Young's modulus $E$ is subjected to a stretching stress $S,$ the elastic energy stored per unit volume of the material is

Show that strain energy per unit volume of a strained wire is $\frac{1}{2}\times stress\times strain$.

The potential energy U between two atoms in a diatomic molecules as a function of the distance x between atoms has been shown in the figure. The atoms are

A metal rod of Young's modulus $2\mathrm{ }\times \mathrm{ }{10}^{10}\mathrm{ }{\mathrm{N}\mathrm{m}}^{–2}$ undergoes an elastic strain of $0.06\%$. The energy per unit volume stored in $\mathrm{J}\mathrm{ }{\mathrm{m}}^{–3}$ is -

A wire suspended vertically from one of its ends is stretched by attaching a weight of $200\mathrm{ }\mathrm{N}$ to the lower end. The weight stretches the wire by $1\mathrm{m}\mathrm{m}$. Then the elastic energy stored in the wire -

A wire suspended vertically from one of its ends is stretched by attaching a weight of $200\mathrm{ }\mathrm{N}$ to the lower end. The weight stretches the wire by $1\mathrm{ }\mathrm{m}\mathrm{m}$. Then the elastic energy stored in the wire -

A metal rod of Young's modulus $2\times {10}^{10}\mathrm{ }{\mathrm{N}\mathrm{m}}^{-2}$ undergoes an elastic strain of $0.06\mathrm{\%}$. The energy per unit volume stored in $\mathrm{J}\mathrm{m}-3$ is -

Energy stored in stretching a string per unit volume is

Energy stored in stretching a string per unit volume is

A wire suspended vertically from one of its ends is stretched by attaching a weight of $200 \mathrm{N}$ to the lower end. The weight stretches the wire by $1 \mathrm{mm}$. Then the elastic energy stored in the wire is