First slide

Elastic Modulie

Question

A wire of length L and cross-section 'A' has Young's modulus of material Y. It is stretched by an amount 'x'. The work done against restoring force is

Easy

A

$\frac{YAx}{2 L}$
B

$\frac{{YAx}^{2}}{L}$
C

$\frac{{YAx}^{2}}{2 L}$
D

$\frac{2 {YAx}^{2}}{L}$

Solution

Total energy = $\frac{1}{2} \times stress \times strain \times volume$
= $\frac{1}{2} \times Y \times {(strain)}^{2} \times volume$
= $\frac{1}{2} Y \times \frac{x^{2}}{L^{2}} \times AL = \frac{1}{2} \frac{{YAx}^{2}}{L}$

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