First slide

Elastic Modulie

Question

An elastic material with Young's modulus Y is subjected to a tensile stress S, elastic energy stored per unit volume of the material is

Easy

A

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

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

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

$\frac{S}{2 Y}$

Solution

$Strain = \frac{Stress}{Y} = \frac{S}{Y}$
Now, energy stored per unit volume $= \frac{1}{2} \times stress \times strain$
$= \frac{1}{2} \times S \times \frac{S}{Y} = \frac{S^{2}}{2 Y}$

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