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 $5 cm$ longer than the copper rod at any temperature? [Given, $\alpha($ steel $)=1.1 \times 10^{-5} \quad{ }^{\circ} C ^{-1}$, $ \left.\alpha(\text { copper })=1.7 \times 10^{-5} \quad{ }^{\circ} C ^{-1}\right] $

• 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, $\alpha \left(s t e e l\right)= \, 1.1\times \left(10\right)^{- 5}℃^{- 1}$
$\alpha \left(c o p p e r\right)=1.7\times \left(10\right)^{- 5}℃^{- 1}$
$\frac{l_{0} \left(s\right)}{l_{0} \left(c\right)}=\frac{\alpha \left(c\right)}{\alpha \left(s\right)}= \, \frac{1.7 \, \times \left(10\right)^{- 5}}{1.1 \times \left(10\right)^{- 5}}=1.545$
$\therefore \, l_{0}\left(s\right)=1.545l_{0}\left(c\right)$
Also, $l_{0}\left(s\right)-l_{0}\left(c\right)=5$
0.545 $l_{0}\left(c\right)=5 \, $
$l_{0}\left(c\right)=\frac{5}{0.545}=9.17 \, cm$
And $l_{0}\left(s\right)=1.545\times 9.17 \, cm \, =14.17 \, cm$