Question

When a force is applied at one end of an elastic wire, it produces a strain E in the wire. If Y is the Young's modulus of the material of the wire, the amount of energy stored per unit volume of the wire is given by

• A. $Y\times E$
• B. $\frac{1}{2}(Y\times E)$
• C. $Y\times E^2$
• D. $\frac{1}{2}(Y\times E^2)$

Answer 1

The correct option is D $\frac{1}{2}(Y\times E^2)$

Energy per unit volume $=\frac{1}{2}\times Stress\times strain$
$=\frac{1}{2}\times (Y\times strain)\times strain$
$=\frac{1}{2}\times Y\times E^2$