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(B) Let $L_s$ and $L_c$ be the lengths of the steel and copper rods at temperature $T$. Given that $L_s - L_c = 5 \ cm$ at all temperatures,the change

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nearly $14 \ cm$ and $9 \ cm$

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(B) Let $L_s$ and $L_c$ be the lengths of the steel and copper rods at temperature $T$. Given that $L_s - L_c = 5 \ cm$ at all temperatures,the change in length for both rods must be equal for any change in temperature $\Delta T$. Therefore,$\Delta L_s = \Delta L_c$. Using the formula for linear expansion $\Delta L = L \alpha \Delta T$,we get: $L_s \alpha_s \Delta T = L_c \alpha_c \Delta T$. $L_s \alpha_s = L_c \alpha_c$. Substituting the given values: $L_s (1.1 	imes 10^{-5}) = L_c (1.7 	imes 10^{-5})$. $L_s / L_c = 1.7 / 1.1 = 17 / 11$. Let $L_s = 17x$ and $L_c = 11x$. Since $L_s - L_c = 5 \ cm$,we have $17x - 11x = 5$,which gives $6x = 5$,so $x = 5/6 \approx 0.833$. Then $L_s = 17 	imes (5/6) \approx 14.16 \ cm$ and $L_c = 11 	imes (5/6) \approx 9.16 \ cm$. These values are nearly $14 \ cm$ and $9 \ cm$.

The length of a steel rod is $5 \ cm$ longer than a copper rod at all temperatures. What are the lengths of the steel and copper rods? (The coefficients of linear expansion for steel and copper are $1.1 \times 10^{-5} /{ }^{\circ} C$ and $1.7 \times 10^{-5} /{ }^{\circ} C$,respectively.)

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