Question

Strain energy per unit volume in a stretched string is

• A. 1/2 $\times$ Stress $\times$ Strain
• B. Stress x Strain
• C. (Stress x Strain)${}^2$
• D. Stress / Strain

Answer 1

The correct option is A 1/2 $\times$ Stress $\times$ Strain

strain energy$=\frac{1}{2}\times stress\times strain$

Work done by a force on a wire

W $=\frac{Ay(\Delta L{)}^2}{2L}$

$=\frac{1}{2}\left(\frac{yA}{}\frac{\Delta L}{L}\right)\Delta L$

$=\frac{1}{2}\left(y\frac{\Delta L}{L}\right)\left(\frac{\Delta L}{L}\right)\left(AL\right)$

$=\frac{1}{2}\left(stress\right)\left(strain\right)\left(volume\right)$

(Work)/(volume)$=\frac{1}{2}\left(stress\right)\left(strain\right)$

Option A