$\begin{array}{1 1}(A)\;.025J\\(B)\;.25J\\(C)\;.035J\\(D)\;0.045J\end{array} $

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$l$=8m

$\Delta l$=1mm=$10^{-3}$m

$a=2mm^2=2\times 10^{-6}m^2$

$V=l\times a=8\times 2\times 10^{-6}=16\times 10^{-6}m^3$

Elastic energy =$\large\frac{1}{2}$$\times (Y)\times (strain)^2\times V$

$\Rightarrow \large\frac{1}{2}$$\times 2\times 10^{11}\times (\large\frac{10^{-3}}{8})^2$$\times 16\times 10^{-6}$

$\Rightarrow \large\frac{16}{64}$$\times 10^{-1}J$

$\Rightarrow .025J$

Hence (A) is the correct answer.

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