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How much energy stored will increase in a steel wire of 5m and $2mm^2$ cross sectional area when force on it increases to 300N from 50N?($Y_{Steel}=2\times 10^{11}N/m^2$)

$\begin{array}{1 1}(A)\;.54J\\(B)\;.32J\\(C)\;2.7J\\(D)\;.27J\end{array} $

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Initial energy density =$\large\frac{1}{2}\times \frac{(stress)^2}{Y}$
$\Rightarrow \large\frac{1}{2}\times (\frac{50}{2\times 10^{-6}})^2\times \frac{1}{2\times 10^{11}}$
$\Rightarrow \large\frac{25000}{16}$
Final energy density =$\large\frac{1}{2}\times (\frac{300}{2\times 10^{-6}})^2\times \frac{1}{2\times 10^{11}}$
$\Rightarrow \large\frac{900000}{16}$
Energy density change =$\large\frac{900,000}{16}-\frac{25000}{16}$
$\Rightarrow \large\frac{875000}{16}$
Energy change =$\large\frac{875000}{16}$$\times$volume
$\Rightarrow \large\frac{875000}{16}$$\times 5\times 2\times 10^{-6}$
$\Rightarrow .54J$
Hence (A) is the correct answer.
answered May 8, 2014 by sreemathi.v

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