a
\(\text { Work }=\Delta K . E\)

\(W_{\text {friction }}+W_{\text {spring }}=0-\frac{1}{2} m v^{2}\)

\(-\frac{90}{100}\left(\frac{1}{2} m v^{2}\right)+W_{\text {Spring }}=-\frac{1}{2} m v^{2}\)

\({W}_{\text {spring }}=-\frac{10}{100} \times \frac{1}{2} {mv}^{2}\)

\(-\frac{1}{2} {kx}^{2}=-\frac{1}{20} {mv}^{2}\)

\(\Rightarrow {k}=\frac{40000 \times(20)^{2}}{10 \times(1)^{2}}=16 \times 10^{5}\)