Question

If '$S$' is stress and '$Y$' is Young?s modulus of material of a wire, the energy stored in the wire per unit volume is:

• A. $2S^2Y$
• B. $\frac{S^{2}}{2Y}$
• C. $\frac{2Y}{S^2}$
• D. $\frac{S}{2Y}$

Answer 1

Answer: (B)

$\frac{S^{2}}{2Y}$

Answer 2

Energy stored in wire $=\frac{1}{2}$ stress $\times$ strain $\times$ volume and Young?s modulus $=\frac{Stress}{Strain} \Rightarrow strain=\frac{S}{Y}$ $\frac{Energy\, stored \,in \,wire }{Volume}=\frac{1}{2}\times Stress\times strain$ $=\frac{1}{2}S\times\frac{S}{Y}=\frac{S^{2}}{2Y}$