An engine is attached to a wagon through a shock absorber of length $1.5 \mathrm{m}.$ The system with a total mass of $40,000 \mathrm{kg}$ is moving with a speed of $72 \mathrm{km} {\mathrm{h}}^{-1}$ when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by $1.0 \mathrm{m}$. If $90\%$ of energy of the wagon is lost due to friction, the spring constant is $\_\_\_\_\_\_\_\_\_\times {10}^5 \mathrm{N} {\mathrm{m}}^{-1}.$

Hence, the correct answer is 16.