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Physics Question on Stress and Strain

Strain energy per unit volume in a stretched string is

A

12×stress×strain\frac{1}{2}\times stress \times strain

B

stress×strainstress \times strain

C

stress×(strain)2stress \times (strain)^2

D

stressstrain\frac{stress} { strain}

Answer

12×stress×strain\frac{1}{2}\times stress \times strain

Explanation

Solution

strain energy =12×=\frac{1}{2} \times stress ×\times strain Work done by a force on a wire W=Ay(ΔL)22L =12(yALΔLL)ΔL =12(yΔLL)(ΔLL)(AL) =12( stress )( strain )( volume ) ( Work )/( volume )=12( stress )( strain )\begin{array}{l} W =\frac{ Ay (\Delta L )^{2}}{2 L } \\\ =\frac{1}{2}\left(\frac{ yA }{ L } \frac{\Delta L }{ L }\right) \Delta L \\\ =\frac{1}{2}\left( y \frac{\Delta L }{ L }\right)\left(\frac{\Delta L }{ L }\right)( AL ) \\\ =\frac{1}{2}(\text { stress })(\text { strain })(\text { volume }) \\\ (\text { Work }) /(\text { volume })=\frac{1}{2}(\text { stress })(\text { strain }) \end{array}