(Solved): In the figure, a constant horizontal force of magnitude \( 12 \mathrm{~N} \) is applied to a unifo ...

In the figure, a constant horizontal force of magnitude \( 12 \mathrm{~N} \) is applied to a uniform solid cylinder by a fishing line wrapped around the cylinder. The mass of the cylinder is \( 10 \mathrm{~kg} \), its radius is \( 0.10 \mathrm{~m} \), and the cylinder rolls smoothly on the horizontal surface. After the rolling is over, you take the same fishing line and apply the same force \( 12 \mathrm{~N} \) with no acceleration. With that, the fishing line changes its length from \( 0.98 \mathrm{~m} \) to \( 0.99 \mathrm{~m} \). If the radius (of the cross-sectional area) of the fishing line is \( 1.2 \mathrm{~mm} \), what is the Young's modulus of this fishing line?