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A bar with a crack at its centre buckles...

A bar with a crack at its centre buckles as a result temperature rise of `32^(@)C`. If the fixed distance `L_(0)` is 3.77m and the coefficient of linear expansion of the bar is `25xx10^(-6)//""^(@)C` find the rise x of the centre.

Text Solution

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Consider one half of the bar, its initial length
`l_(0)=L_(0)/2`
Its length after increase in temperature `Deltat`,
`l=l_(0)(1+alphaDeltaT)`
By Pythogoras theorem `x^(2)=l^(2)-l_(0)^(2)`
`l^(2)=l_(0)^(2)(1+2alphaDeltaT)orx=l_(0)sqrt(2alphaDeltaT)`
= `3.77/2sqrt(2(25xx10^(-6)xx32))=7.5xx10^(-2)m`
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