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A 30"cm" long metal rod expands by 0.065...

A `30"cm"` long metal rod expands by `0.0650"cm"` when its temperature is raised from `0^(@)C` to `100^(@)C`. A second rod of different metal and of the same length expands by `0.0350"cm"` for the same rise in temperature. A third composite rod, also `30"cm"` long, is made-up of pieses of each of the above metals placed end to end and expands by `0.0580"cm"` when temperature is increased from `0^(@)C` to `100^(@)C`. Find the length of the longer portion of the composite bar in cm at `0^(@)C`.

Text Solution

Verified by Experts

`alpha_(1)=(0.065)/(30xx100)`
`alpha_(2)=(0.035)/(30xx100)`
`Deltal=l_(1)a_(1)DeltaT+(30-l_(1))alpha_(2)DeltaT`
`0.058=l_(1)xx(0.065)/(3000)+(30-l_(1))xx(0.035)/(3000)`
`1.74=0.065l_(1)+1.05-0.035l_,`
`0.69=+0.03l_(1)`
`l_(1)=23" cm ",l_(2)=7" cm "`
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