Answer
$k = 49 \times 10^{3} \mathrm{N} / \mathrm{m}$
Work Step by Step
The tension force $kx$ of the spring equals the weight $mg$ as they are in the opposite direction
\begin{gather*}
kx = mg\\
k = \dfrac{mg}{x} \\
k = \dfrac{mg}{x}\\
k= \frac{(500 \mathrm{kg})\left(9.8 \mathrm{m} / \mathrm{s}^{2}\right)}{0.10 \mathrm{m}}\\
k= \boxed{49 \times 10^{3} \mathrm{N} / \mathrm{m}}
\end{gather*}
