Elastic behaviour of solids

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Question

A steel wire of cross-sectional area 2mm² and Young’s modulus 2 x10¹¹N / m² is stretched longitudinally by a force of 200 N. The elastic potential energy stored per unit volume in the string is n × 10⁴. Find the value of ‘n’.

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Solution

EPE per unit volume $= \frac{1}{2}$ × stress× strain = $\frac{{(s t r e s s)}^{2}}{2 Y} = \frac{F^{2}}{2 Y A^{2}} = \frac{200^{2}}{2 \times 2 \times 10^{11} \times 4 \times 10^{- 12}} J / m^{3} = 2.5 \times 10^{4} J / m^{3}$

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