Mechanical Properties of Solids - Result Question 10
11. When an elastic material with Young’s modulus $Y$ is subjected to stretching stress $S$, elastic energy stored per unit volume of the material is
(a) $YS / 2$
(b) $S^{2} Y / 2$
(c) $S^{2} / 2 Y$
(d) $S / 2 Y$
[1989]
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Solution:
- (c) Energy stored per unit volume
$=\frac{1}{2} \times$ stress $\times$ strain
$=\frac{1}{2} \times$ stress $\times($ stress $/$ Young’s modulus $)$
$=\frac{1}{2} \times(\text{ stress })^{2} /($ Young’s modulus $)=\frac{S^{2}}{2 Y}$
