First slide

Elastic Modulie

Question

The elastic energy per unit volume in terms of longitudinal strain $σ$ and Young's modulus Y is:

Moderate

A

$\frac{{Yσ}^{2}}{2}$
B

$\frac{1}{2} Y . σ$
C

$2 {Yσ}^{2}$
D

$2 Yσ$

Solution

The elastic potential energy per unit volume = $\frac{1}{2} stress \times strain = \frac{1}{2} Y strain \times strain$
= $\frac{1}{2} Y {(strain)}^{2} = \frac{1}{2} {Yσ}^{2}$

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