Question

An iron rod of length 50 cm is joined at an end to an aluminum rod of length 100cm. All measurement refer to ${20}^{\circ }C$. Find the length of the composite system at ${100}^{\circ }C$ and its average coefficient of linear expansion. The coefficient of linear expansion of iron and aluminum are $12\times {10}^{-6}{/}^{\circ }C$ and $24\times {10}^{-6}{/}^{\circ }C$ respectively.

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

The length of the iron rod at ${100}^{\circ }C$ is
$Thelengthofthealuminumrodat{100}^{\circ }Cis{l}_2=\left(100cm\right)[1+(24\times {10}^{-6}{/}^{\circ }C\left)\right({100}^{\circ }C-{20}^{\circ }C\left)\right]=100.192cmThelengthofcompositesystemat{100}^{\circ }Cis50.048+100.192=150.24cm$
The length of the composite system at ${20}^{\circ }C$ is 150 cm. So, the average coefficient of linear expansion of the composite rod is
$\alpha =\frac{0.24cm}{150cm\times ({100}^{\circ }C-{20}^{\circ }C)}=20\times {10}^{-6}{/}^{\circ }C$