As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of 45° with the load axis. The length of the wire is 62.8 cm and its diameter is 4 mm. The Young's modulus is found to be $$x \times 10^4$$ N m$$^{-2}$$. The value of $$x$$ is _____.

$$Y = \frac{\text{Stress}}{\text{Strain}} = \frac{F / A}{\Delta L / L} = \left( \frac{F}{\Delta L} \right) \cdot \frac{L}{A}$$

$$\text{Slope} = \frac{\text{Change in Extension}}{\text{Change in Load}} = \frac{\Delta L}{F} = \tan(45^\circ) = 1$$

$$A \approx 4 \times 3.14 \times 10^{-6} = 12.56 \times 10^{-6} \text{ m}^2$$

$$Y = \left( \frac{F}{\Delta L} \right) \cdot \frac{L}{A}$$

$$Y = (1) \cdot \frac{0.628}{12.56 \times 10^{-6}}$$

$$Y = \frac{0.628 \times 10^6}{12.56} = 0.05 \times 10^6$$

$$Y = 5 \times 10^4 \text{ N m}^{-2}$$

$$x = 5$$