A steel wire `AB` of length `85cm` at `10^(@)C` is fixed rigidly at points `A` and `B` in an aluminium frame as shown. If the temperature of the system is raised to `110^(@)C` , what extra stress will be produced in the wire relative to aluminium frame. Assume that coefficient of linear expansion for aluminium and steel are `23xx10^(-6)//^(@)C` and `11xx10^(-6)//^(@)C` respectively and Young's moduls for steel is `2xx10^(11)` pa.

Explanation

As `alpha_(a)gtalpha_(s)` , on heating, aluminium frame will expand more than the steel wire
Thermal strain in steel wire realtive to aluminium wire
`=(alpha_(a)-alpha_(s))Deltatheta`
`=(23-11)xx10^(-6)xx[110-10]`
`=1.2xx10^(-3)`
Thermal stress=Y `xx`Thermal strain
`=2xx10^(11)xx1.2xx10^(-3)`
`=2.4xx10^(8)N//m^(2)` .