Question

Elastic potential energy stored in a steel rod of mass m = 4 $kg$ under strain of ${10}^{-3}$ is ____. [density and Young's modulus for steel are $8\times {10}^{3}kg/m^2$ and $2\times {10}^{11}N/m^2$]

• A. 100 J
• B. 2000 J
• C. 25 J
• D. 50 J

Answer 1

The correct option is D 50 J

Energy U =$\frac{1}{2}\text{stress}\times \text{strain}\times \text{Vol}$

$U=\frac{1}{2}Y{\text{(strain )}}^2\times \frac{m}{\rho }=\frac{1}{2}\times 2\times {10}^{11}{\left({10}^{-3}\right)}^2\times \frac{4}{8000}$

U= 50 J