1.

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.

Answer»

Solution :`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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