Question

What should be the lengths of steel and copper rod so that the length of steel rod is $5 cm$ longer then the copper rod at all the temperatures? Coefficients of linear expansion for copper and steel are 1.7 and 1.1 :

• A. $2.17,14.17 cm$
• B. $9.17,14.17 cm$
• C. $9.17,18.17 cm$
• D. $3.17,5.17 cm$

Answer 1

Answer: (B)

It is given that the difference in length of the two rods is always $5 cm$. Thus the expansion in both the rods must be same for all temperatures. Thus we can say that at all temperature differences, we have
$\Delta L _{ Cu }=\Delta L _{\text {steel }}$
or $\alpha_{C u} \ell_{1} \Delta t=\alpha_{s t} \ell_{2} \Delta t $
$\left[\right.$ If $\ell_{1}$ and $\ell_{2}$ are the initial lengths of $Cu$ and steel rods]
or $\alpha_{C u} \ell_{1}=\alpha_{s t} \ell_{2}$
or $1.7 \ell_{1}=1.1 \ell_{2} \ldots .(1)$
It is given that $\ell_{2}-\ell_{1}=5 cm \ldots$ (2)
$\left(\frac{1.7}{1.1}-1\right) \ell_{1}=5 cm$
or $\ell_{1}=\frac{5 \times 1.1}{0.6}=9.17 cm$
Now from equation (2) $\ell_{2}=14.17 cm$