\(\frac{F L}{A Y}=\Delta x\)
Since \(A, Y\) remain constant in given case We can say
\(F L \propto \Delta x\)
or \(\frac{F_1 L_1}{F_2 L_2}=\frac{\Delta x_1}{\Delta x_2}\) \(\left\{\begin{array}{l}F_1=200 \,N \\ \Delta x_1=1 \,mm \\ \Delta x_2=10.02 \,m -10 \,m =0.02 \,m =20 \,mm \\ L_1=1 \,m \\ L_2=10 \,m \end{array}\right.\)
Substitute the values
\(\frac{200 \times 1}{F_2 \times 10}=\frac{1 \,mm }{20 \,mm }\)
\(F_2=400 \,N\)