A brass rod of length 50cm and diameter `3.0` mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at `250^(@)C`, if the original lengths are at `40.0^(@)C` ? Is there a thermal stress developed at the junction ? The ends of the rod are free to expand (Co-efficient of linear expansion of brass `=2.0xx10^(-5)K^(-1)`, steel `=1.2xx10^(-5)K^(-1)`.

Explanation

`DeltaL_(1)=L_(1)alpha_(1)DeltaT=50xx(2.10xx10^(-5))(250-40)=0.2205cm`
`DeltaL_(2)=L_(2)alpha_(2)DeltaT`
`=50xx(1.2xx10^(-5))(250-40)=0.216cm`
`:.` Change in length of combined rod `=DeltaL_(1)+DeltaL_(2)`
`=0.220+0.126=0.346cm`