#### Answer

Young's modulus for the rope is $5.5\times 10^9~N/m^2$

#### Work Step by Step

We can find Young's modulus for the rope as:
$Y = \frac{F/A}{\Delta~L/L}$
$Y = \frac{F~L}{A~\Delta L}$
$Y = \frac{(70~kg)(9.80~m/s^2)(50~m)}{(\pi)(5.0\times 10^{-3}~m)^2(0.080~m)}$
$Y = 5.5\times 10^9~N/m^2$
Young's modulus for the rope is $5.5\times 10^9~N/m^2$.