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Railway lines are laid with gaps to allo...

Railway lines are laid with gaps to allow for expansion. If the gap betweeen steel rails 60 m long be 3.60 cm at `10^(@)C`, then at what temperature will the lines just touch? Coefficient of linear expansion of steel `=11xx10^(-6) .^(@)C^(-1)`.

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The correct Answer is:
50
As the rails expand in both directions, so the gap between two rails is filled by the expansion of half length of each rail. Equivalently, we can take the expansion of one rail in one direction to fill the gap
`therefore l=66 m,Deltal=3.63 xx 10^(-2)m` ,
`alpha=11 xx 10^(-6)""^@ C^(-1)`
As `Delta l =l alpha DeltaT`
`Delta T=(Delta l)/(l alpha)=(3.36 xx 10^(-2))/(66 xx 11 xx 10^(-6))=50^@C`
Final temperature = initial temperature + `Delta T =10+50=60^@C`
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