Question

A wire of natural length $l,$ Youngs modulus $Y$ and area of cross-section $A$ is extended by $x$ . Then the energy stored in the wire is given by

• A. $\frac{1}{2}\frac{YA}{l}{{x}^{2}}$
• B. $\frac{1}{3}\frac{YA}{l}{{x}^{2}}$
• C. $\frac{1}{2}\frac{Yl}{A}{{x}^{2}}$
• D. $\frac{1}{2}\frac{YA}{{{l}^{2}}}{{x}^{2}}$

Answer 1

Answer: (A)

$\frac{1}{2}\frac{YA}{l}{{x}^{2}}$

Answer 2

Energy stored in the wire
$U=\frac{1}{2}Y\times {{(strain)}^{2}}\times volume$
Or $U=\frac{1}{2}Y\times {{\left( \frac{x}{l} \right)}^{2}}\times Al$
Or $U=\frac{1}{2}\frac{Y{{x}^{2}}}{l}\times A$
Or $U=\frac{1}{2}\frac{YA}{l}{{x}^{2}}$