\(\text { Modulus of rigidity }(G)=\frac{\text { Force } \times \text { Length }}{\text { Area } \times \text { Lateral displacement }}=\frac{F L}{A \times \Delta x}\)

\(F=10 \,kN =10 \times 10^3 \,N\)

\(L=4 \,cm =0.04 \,m\)

\(A=1 \,cm ^2=1 \times 10^{-4} \,m ^2\)

\(G=8 \times 10^{11}\,N / m ^2\)

Substituting values

\(8 \times 10^{11}=\frac{10 \times 10^3 \times 0.04}{1 \times 10^{-4} \times \Delta x}\)

\(\Delta x=\frac{10 \times 10^3 \times 0.04}{1 \times 10^{-4} \times 8 \times 10^{11}}=5 \times 10^{-6} \,m\)