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Coefficient of linear expansion of brass and steel rods are $\alpha_{1}$ and $\alpha_{2}$ . Lengths of brass and steel rods are $\l_{1}$ and $\l_{2}$ respectively. If ( $\l_{2}$ - $\l_{1}$ ) is maintained same at all temperatures, which one of the following relations holds good?
Option: 1
$\alpha_{1}\l_{2}=\alpha_{2}\l_{1}$

Option: 2
$\alpha_{1}\l_{2}^{2}=\alpha_{2}\l_{1}^{2}$

Option: 3
$\alpha_{1}^{2}\l_{2}=\alpha_{2}^{2}\l_{1}$

Option: 4
$\alpha_{1}\l_{1}=\alpha_{2}\l_{2}$

Answers (1)

best_answer

As we learnt in

Change in Length -

$Delta L=L_{0}(alpha Delta T)$

- wherein

$Delta L=L-L_{0}$

$L-L_{0}=$ Change in length

$Delta T=T-T_{0}$

$T-T_{0}=$ Change in temperature

$l_{2}-l_{1}$ is maintained same at all temperature if $\Delta l_{2}=\Delta l_{1}$

$\Rightarrow \ l_{2}. \alpha _{2}\Delta T=l_{1} \alpha _{1}\Delta T$

or $\Rightarrow \ l_{1}. \alpha _{1}=l_{2} \ \alpha _{2}$

Posted by

sudhir.kumar

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