Properties Of Matter

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 ________ \(\times 10^{-4} \mathrm{~m}^2\) (consider \(x<<\mathrm{L}\) ).

(given : \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\))