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A railway track (made of iron) is laid i...

A railway track (made of iron) is laid in winter when the average temperature is `18^(@)C`. The track consists of sections of 12.2 m placed one after the other. How much gap should be left between two such sections so that there in no compression during summer when the maximum temperature goes to `48^(@)C`? Coefficient of linear expansion of iron `= 11 xx 10^(-5) @C(-1)`.

Text Solution

Verified by Experts

`L_0=12m` alpha =11xx10^-6/^0C`
`t _w= 18^0C` t_s=48^0C`
`L_w= L_0(1+alpha Delta t_w)`
` =12(1+11xx 10^-6xx 18)`
`=12.006336m`
`:. Delta L= 12.006336-12.002376`
`=0.00396m ~~0.4cm `
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