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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


Option: 2


Option: 3


Option: 4


Answers (1)


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}


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