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Physics Question on Stress and Strain

The energy stored per unit volume in copper wire, which produces longitudinal strain of 0.1% is (Y=1.1×103Nm−2)(Y =1.1\times10^3 Nm^{-2})

A

11×103Jm−311\times10^3 Jm^{-3}

B

5.5×103Jm−35.5\times10^3 Jm^{-3}

C

5.5×104Jm−35.5\times10^4 Jm^{-3}

D

11×104Jm−311\times10^4 Jm^{-3}

Answer

5.5×104Jm−35.5\times10^4 Jm^{-3}

Explanation

Solution

Elastic potential energy per unit volume of the wire u=12×stress×strainu=\frac{1}{2}\times stress\times strain =12×(Young′smodulus×strain)×strain=\frac{1}{2}\times(Young's modulus\times strain)\times strain =12×(Y)×(strain)2=\frac{1}{2}\times(Y)\times(strain)^2 ∴\therefore u=12×1.1×1011×(0.1100)2u=\frac{1}{2}\times1.1\times10^{11}\times\left(\frac{0.1}{100}\right)^2 =5.5×104Jm−3=5.5\times10^4Jm^{-3}