A wire of cross sectional area A, modulus of elasticity $2 \times 10^{11} \mathrm{~Nm}^{-2}$ and length $2 \mathrm{~m}$ is stretched between two vertical rigid supports. When a mass of $2 \mathrm{~kg}$ is suspended at the middle it sags lower from its original position making angle $\theta=\frac{1}{100}$ radian on the points of support. The value of A is $\underline{\hspace{2cm}}$$\times 10^{-4} \mathrm{~m}^2$(consider $x\lt \lt \mathrm{L}$). (given : $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$)