Question

A metal rod of Young's modulus $2\times {10}^{10}N{m}^{-2}$ undergoes an elastic strain of $0.06\%$. The energy per unit volume stored in $J{m}^{-3}$ is

• A. $3600$
• B. $7200$
• C. $10800$
• D. $14400$

Answer 1

The correct option is A $3600$

Energy per unit volume$=\frac{1}{2}\times Stress\times Strain=\frac{1}{2}\times (Strain\times Y)\times Strain=\frac{1}{2}\times Y\times {\left(Strain\right)}^2$
Thus, we get, $0.5\times 2\times {10}^{10}\times {\left(0.0006\right)}^2=3600$