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(A) Let $L_s$ and $L_c$ be the lengths of the steel and copper rods at a certain temperature. The difference in their lengths is given as $L_s - L_c =

Vedclass · Accepted Answer

$17/11$

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(A) Let $L_s$ and $L_c$ be the lengths of the steel and copper rods at a certain temperature. The difference in their lengths is given as $L_s - L_c = 4 \ cm$, which remains constant at any temperature.This implies that the change in length of both rods due to a change in temperature $\Delta T$ must be equal.Therefore, $\Delta L_s = \Delta L_c$.Using the formula for linear expansion $\Delta L = \alpha L \Delta T$, we get $\alpha_s L_s \Delta T = \alpha_c L_c \Delta T$.Canceling $\Delta T$ from both sides, we have $\alpha_s L_s = \alpha_c L_c$.Substituting the given values: $(1.1 	imes 10^{-5}) L_s = (1.7 	imes 10^{-5}) L_c$.Thus, the ratio $\frac{L_s}{L_c} = \frac{1.7 	imes 10^{-5}}{1.1 	imes 10^{-5}} = \frac{17}{11}$.

Find the ratio of the length of a steel rod and a copper rod if the steel rod is $4 \ cm$ longer than the copper rod at any temperature. $[$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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