The length of steel rod is 5 cm longer than the copper rod at all temperatures. The length of the steel and…

The constant length difference condition $L_s(T) - L_c(T) = 5\text{cm}$ must hold for all temperatures. Applying thermal expansion formulas $L(T) = L_0(1 + \alpha\Delta T)$ yields:

$(L_s - L_c) + (L_s\alpha_s - L_c\alpha_c)\Delta T = 5$

For temperature independence, both $L_s - L_c = 5$ and $L_s\alpha_s = L_c\alpha_c$ must be satisfied.

Substituting $L_s = L_c + 5$ into the second equation:

$(L_c + 5)\alpha_s = L_c\alpha_c$

$L_c = \frac{5\alpha_s}{\alpha_c - \alpha_s} = \frac{5 \times 1.1 \times 10^{-5}}{(1.7 - 1.1) \times 10^{-5}} = \frac{5.5}{0.6} \approx 9.17\text{cm}$

Thus $L_s = L_c + 5 \approx 14.17\text{cm}$.

These values correspond to nearly 14 cm and 9 cm, matching option B.