First, plot the data shown as points.
The points are (0,0), (1.4, 10), (2.8, 20), (4.2, 30), (4.9, 35), (5.8, 40), and (8, 45).
The graph shows a proportional part (a straight line) and a curvy part. So, the limit of proportionality is shown at the end of the straight line segment. The image below shows this limit.
The gradient of the straight-line portion refers to the slope. Let's use the points (1.4, 10) and (2.8, 20).
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{20-10}{2.8-1.4}=\frac{10}{1.4}\approx7.14[/tex]
Therefore, the gradient is 7.14.
The Young modulus formula is
[tex]E=\frac{\frac{F}{A}}{\frac{\Delta l}{l}}[/tex]
Let's use the greater force and the greater extension.
[tex]E=\frac{\frac{45N}{7\times10^{-8}m^2}}{\frac{8\times10^{-3}m}{2m}}=1.6\times10^{11}[/tex]
Therefore, Young Modulus is 1.6x10^11.
