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  4. A steel wire of length 2 m is stretched through 2 mm. What is elastic potential energy stored in a wire of cross-sectional area 4 mm 2 in stretched condition (Y=2 × 1011 Nm -2)

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Q. A steel wire of length $2\, m$ is stretched through $2\, mm$. What is elastic potential energy stored in a wire of cross-sectional area $4 \,mm ^{2}$ in stretched condition $\left(Y=2 \times 10^{11}\, Nm ^{-2}\right)$

Solution:

$\frac{\Delta l}{l}=\frac{2}{2} \times 10^{-3}=10^{-3}$
Stress $=Y \times$ strain $=2 \times 10^{11} \times 10^{-3}$
$=2 \times 10^{8} \,Nm ^{2}$
Volume $=4 \times 10^{-6} \times 2=8 \times 10^{-6} \,m ^{3}$
Energy stored $=\frac{1}{2} \times$ stress $\times$ strain $\times$ volume
$=\frac{1}{2} \times 2 \times 10^{8} \times 10^{-3} \times 8 \times 10^{-6}=0.8\, J$