Question

What should be the lengths of a steel and copper rod at $0{}^{\circ }C$ so that the length of the steel rod is $5cm$ longer than the copper rod at any temperature? [Given, $\alpha ($ steel $)=1.1\times 10^{-5}{}^{\circ }{C}^{-1}$, $\alpha (\text{ copper })=1.7\times 10^{-5}{}^{\circ }{C}^{-1}]$

• A. $14.17cm;9.17cm$
• B. $9.17cm,14.17cm$
• C. $28.34cm;18.34cm$
• D. $14.17cm,18.34cm$

Answer 1

Answer: (A)

Here, $\alpha \left(steel\right)=1.1\times {\left(10\right)}^{-5}{℃}^{-1}$
$\alpha \left(copper\right)=1.7\times {\left(10\right)}^{-5}{℃}^{-1}$
$\frac{l_0\left(s\right)}{l_0\left(c\right)}=\frac{\alpha \left(c\right)}{\alpha \left(s\right)}=\frac{1.7\times {\left(10\right)}^{-5}}{1.1\times {\left(10\right)}^{-5}}=1.545$
$\therefore l_0\left(s\right)=1.545l_0\left(c\right)$
Also, $l_0\left(s\right)-l_0\left(c\right)=5$
0.545 $l_0\left(c\right)=5$
$l_0\left(c\right)=\frac{5}{0.545}=9.17cm$
And $l_0\left(s\right)=1.545\times 9.17cm=14.17cm$