Question:
The elastic behavior of a material for linear stress to linear strain is given in the figure. The energy density for a linear strain of \(4\times10^{-4}\) is
center
The elastic behavior of a material for linear stress to linear strain is given in the figure. The energy density for a linear strain of \(4\times10^{-4}\) is
center
Show Hint
Energy density equals the area under the stress-strain graph.
For linear elastic region:
\[
u=\frac12 \sigma \epsilon
\]
Updated On: Jun 17, 2026
- \(20000\ \text{J m}^{-3}\)
- \(16000\ \text{J m}^{-3}\)
- \(12000\ \text{J m}^{-3}\)
- \(8000\ \text{J m}^{-3}\)
Show Solution
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The Correct Option is B
Solution and Explanation
Concept:
Energy density stored in a stretched material:
\[
u=\frac12(\text{stress})(\text{strain})
\]
From graph:
At strain:
\[
4\times10^{-4}
\]
stress is:
\[
80\times10^6\ \text{N/m}^2
\]
Step 1: Apply formula for energy density. \[ u=\frac12 \times 80\times10^6 \times 4\times10^{-4} \] \[ u=\frac12 \times 32000 \] \[ u=16000\ \text{J/m}^3 \] Hence, \[ \boxed{16000\ \text{J/m}^3} \]
Step 1: Apply formula for energy density. \[ u=\frac12 \times 80\times10^6 \times 4\times10^{-4} \] \[ u=\frac12 \times 32000 \] \[ u=16000\ \text{J/m}^3 \] Hence, \[ \boxed{16000\ \text{J/m}^3} \]
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