Question

An iron rod of length $50cm$ is joined to an aluminium rod of length $100cm$. All measurements refer to ${20}^{\circ }C$. The coefficient of linear expansion of iron and aluminium are $12\times {10}^{-6}{/}^{\circ }C$ and $24\times {10}^{-6}{/}^{\circ }C$ respectively. The average coefficient of composite system at ${100}^{0}C$ is :

• A. $36\times {10}^{-6}{/}^{\circ }C$
• B. $12\times {10}^{-6}{/}^{\circ }C$
• C. $20\times {10}^{-6}{/}^{\circ }C$
• D. $48\times {10}^{-6}{/}^{\circ }C$

Answer 1

The correct option is C $20\times {10}^{-6}{/}^{\circ }C$

We have the length of the iron rod at ${100}^{o}C$ as

$L_1=50[1+12\times {10}^{-6}\times 80]=50.048cm$

and the length of the aluminium rod will be

$L_2=100[1+24\times {10}^{-6}\times 80]=100.192cm$

Thus we get the length of the composite system as:

$50.048+100.192=150.24cm$

At ${20}^{o}C$ the length of the composite system is $150cm$.

Thus we get,

$\alpha =\frac{0.24}{150\times (100-20)}$

$=20\times {10}^{-6}{/}^{o}C$