A composite rod is made of a steel segment of length 0.6 m (α=1.2×10^-5 K^-1, Y=2×10^11 N m^-2) joined end to end to a copper-like segment of length…

The walls fix the total length, so the total thermal expansion is cancelled by the elastic compression produced by the same force $F$ in both segments (they are in series, so the force is common). Free thermal expansion: $\Delta L_{th}=(0.6\times1.2\times10^{-5}+0.4\times1.7\times10^{-5})\times100=1.4\times10^{-3}\ \mathrm m$. Elastic compression: $\Delta L_{el}=\dfrac{F}{A}\left(\dfrac{L_1}{Y_1}+\dfrac{L_2}{Y_2}\right)=\dfrac{F}{4\times10^{-4}}\left(3\times10^{-12}+4\times10^{-12}\right)=1.75\times10^{-8}F$. Setting equal: $F=\dfrac{1.4\times10^{-3}}{1.75\times10^{-8}}=8.0\times10^{4}\ \mathrm N=80\ \mathrm{kN}$. The other options come from using a single modulus for the entire rod: steel only gives $112\ \mathrm{kN}$, copper only $56\ \mathrm{kN}$, and the mean modulus $1.5\times10^{11}$ gives $84\ \mathrm{kN}$; none accounts correctly for the series combination.