d
\(\begin{array}{l}
v = \sqrt {2 \times 10}  \times 100\\
\,\,\,\, = 20\sqrt 5 \\
COLM \to \,{v_p} = \frac{{1 \times 20\sqrt 5 }}{4}\\
COTME \to \\
\frac{1}{2} \times 4 \times {\left( {5\sqrt 5 } \right)^2} + \frac{1}{2}1.25 \times {10^6}{\left( {\frac{{30}}{k}} \right)^2}
\end{array}\)

\(\begin{array}{l}
 =  - 4 \times 10 \times \left( {n - \frac{{30}}{k}} \right) + \frac{1}{2}k{n^2}\\
 \Rightarrow \,\,250 + \frac{{900}}{{2 \times 1.25 \times {{10}^6}}}\\
\,\, =  - 40x + \frac{{1200}}{k} + \frac{1}{2}k{x^2}\\
 \Rightarrow \,x = 2\,cm
\end{array}\)