Elastic behaviour of material for linear streass and linear strain, is shown in figure. energy densi

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8.Mechanical Properties of Solids

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The elastic behaviour of material for linear streass and linear strain, is shown in the figure. The energy density for a linear strain of $5 \times 10^{-4}$ is $\dots \; kJ / m ^{3}$. Assume that material is elastic upto the linear strain of $5 \times 10^{-4}$.

A

$35$

B

$-35$

C

$25$

D

$-25$

(JEE MAIN-2022)

Solution

$y =\frac{\text { stress }}{\text { strain }}=2.0 \times 10^{10}$

Energy density $=\frac{1}{2} \; stress \; \times \; strain$

$=\frac{1}{2}(\text { strain })^{2} y =\frac{1}{2}\left(5 \times 10^{-4}\right)^{2} \times 20 \times 10^{10}$

$=25 \times 10^{2} \times 10=25 \frac{ kJ }{ m ^{3}}$

Ans. $25$

Standard 11

Physics

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