The elastic energy stored per unit volume in terms of longitudinal strain ' $\epsilon$ ' and Young's modulus…

The elastic energy stored per unit volume in terms of longitudinal strain ' $\epsilon$ ' and Young's modulus ' $Y$ ' is
  1. $\frac{Y \epsilon^2}{2}$
  2. $\frac{1}{2} Y \in$
  3. $2 \mathrm{Y} \in^2$
  4. $2 \mathrm{Y} \in$

Solution

The elastic potential energy per unit volume is $\mathrm{u}=\frac{1}{2} \times \sigma \times \varepsilon$
By Hook's law, $\sigma=\mathrm{Y} \varepsilon$ $\therefore \mathrm{x}=\frac{1}{2} \times \mathrm{Y} \varepsilon \times \varepsilon=\frac{\mathrm{Y} \varepsilon^2}{2}$

Asked in: AP EAMCET 2024 (21 May Shift 1)

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