Q. What should be the lengths of a steel and copper rod at 0$℃\ $ so that the length of the steel rod is 5 cm longer than the copper rod at any temperature? $\alpha\ $(Steel) = 1.1 $\times 10^{- 5}℃^{- 1}$ $\alpha\ ($Copper)= $1.7\ \times 10^{- 5}℃^{- 1}$
A) 14.17 cm; 9.17 cm
B) 9.17 cm, 14.17 cm
C) 28.34 cm; 18.34 cm
D) 14.17 cm, 18.34 cm
Explanation
(a) Here, $\alpha(steel) = \ 1.1 \times 10^{- 5}℃^{- 1}$
$\alpha(copper) = 1.7 \times 10^{- 5}℃^{- 1}$
$\frac{l_{0}(s)}{l_{0}(c)} = \frac{\alpha(c)}{\alpha(s)} = \ \frac{1.7\ \times 10^{- 5}}{1.1 \times 10^{- 5}} = 1.545$
$\therefore\ l_{0}(s) = 1.545l_{0}(c)$
Also, $l_{0}(s) - l_{0}(c) = 5$
0.545$l_{0}(c) = 5\ $
$l_{0}(c) = \frac{5}{0.545} = 9.17\ cm$
And $l_{0}(s) = 1.545 \times 9.17\ cm\ 14.17\ cm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.