AP EAMCET · PHYSICS · Mechanical Properties of Solids
The elastic energy stored per unit volume in terms of longitudinal strain ' \(\epsilon\) ' and Young's modulus ' \(Y\) ' is
- A \(\frac{Y \epsilon^2}{2}\)
- B \(\frac{1}{2} Y \in\)
- C \(2 \mathrm{Y} \in^2\)
- D \(2 \mathrm{Y} \in\)
Answer & Solution
Correct Answer
(A) \(\frac{Y \epsilon^2}{2}\)
Step-by-step Solution
Detailed explanation
The elastic potential energy per unit volume is \(\mathrm{u}=\frac{1}{2} \times \sigma \times \varepsilon\) By Hook's law, \(\sigma=\mathrm{Y} \varepsilon\) \(\therefore \mathrm{x}=\frac{1}{2} \times \mathrm{Y} \varepsilon \times \varepsilon=\frac{\mathrm{Y} \varepsilon^2}{2}\)
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