First slide

Elastic behaviour of solids

Question

A uniform wire of cross-sectional area A and Young's modulus Y is stretched within the elastic limit. If S is the stress in the wire, the elastic energy density stored in the wire in terms of the given parameters is

Moderate

A

$\frac{S}{2 Y}$
B

$\frac{2 Y}{S^{2}}$
C

$\frac{S^{2}}{2 Y}$
D

$\frac{S^{2}}{Y}$

Solution

Let the strain be $ε$ . Then $Y = \frac{S}{ε} or ε = \frac{S}{Y}$ . Now energy density $= \frac{1}{2} stress \times strain = \frac{1}{2} \times S \times \frac{S}{Y} = \frac{S^{2}}{2 Y}$ . Hence the correct choice is (3).

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