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Two steel rods and an aluminium rod of e...

Two steel rods and an aluminium rod of equal length `l_0` and equal cross- section are joined rigidly at their ends as shown in the figure below. All the rods are in a state of zero tension at `0^@ C`. Find the length of the system when the temperature is raised to `theta`. Coefficient of linear expansion of aluminium and steel are `alpha_(a)` and `alpha_(s)` respectively. Young's modulus of aluminium is `Y_(a)` and of steel is `Y_(s)`.

Text Solution

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The correct Answer is:
`l_(0)[1+(alpha_(a)+2alpha_(s)Y_(s))/(Y_(a)+2Y_(s)).Delta theta]`
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