The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of 5 × 10−4 is __________ kJ/m3. Assume that material is elastic upto the linear strain of 5 × 10−4. Numerical answer type. Work it out, then open the answer.

Answer: 25. From the graph, strain 10⁻¹⁰ at stress 20 N/m², so Y = 2010⁻¹⁰ = 2 × 10¹¹ N/m². u = 1/2Yε² = 1/2 × 2 × 10¹¹ × (5 × 10⁻⁴)² u = 2.5 × 10⁴ J/m³ = 25 kJ/m³ So the answer is 25.

The elastic behaviour of material for linear stress and linear… | JEE Main 2022 (26 Jun, Shift 1)

Q6JEE Main 2022 · 26 JUN · SHIFT 1Medium

Elastic Potential Energy

The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of 5 $\times$ 10−4 is __________ kJ/m3. Assume that material is elastic upto the linear strain of 5 $\times$ 10−4.

Numerical answer type. Work it out, then open the answer.

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Answer: 25

From the graph, strain $10^{-10}$ at stress $20\text{ N/m}^2$ , so $Y = \dfrac{20}{10^{-10}} = 2 \times 10^{11}\text{ N/m}^2$ .
$u = \dfrac{1}{2}Y\varepsilon^2 = \dfrac{1}{2} \times 2 \times 10^{11} \times (5 \times 10^{-4})^2$
$u = 2.5 \times 10^4\text{ J/m}^3 = 25\text{ kJ/m}^3$
So the answer is 25.

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