Question

Select the correct option given below:
At ${50}^{o}C$, a brass rod has a length $50cm$ and a diameter 2mm.it is joined to a steel rod of the same length and diameter at the same temperature. The change in the length of the composite rod when it is heated to ${250}^{o}C$ is (Coefficient of linear expansion of brass

$=2.0\times {10}^{-5}$ $C^{-1}$, the coefficient of linear expansion of steel $=1.2\times {10}^{-5}{C}^{-1}$

• A. $0.28cm$
• B. $0.30cm$
• C. $0.32cm$
• D. $0.34cm$

Answer 1

The correct option is C $0.32cm$

Change in length of the brass rod is given by:

$\Delta L_b={\alpha }_b{L}_b\Delta T$

$\Rightarrow 2.0\times 10{-5}^o{C}^{-1}\times 50cm\times ({250}^{o}C-{50}^{o}C)$
$\Rightarrow 0.2cm$

Change in length of the steel rod is
$\Delta L_s={\alpha }_s{L}_s\Delta T$
$=1.2\times {10}^{-5}{}^o{C}^{-1}\times 50cm\times ({250}^{o}C-{50}^{o}C)$
$=0.12cm$

$\therefore$ Change in length of the combined rod

$=\Delta L_b+\Delta L_s$

$=0.2cm+0.12cm=0.32cm$