A brass rod of length `50 cm` and diameter `3.0 cm` 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 length are at `40.0^(@)C`?
(Coefficient of linear expansion of brass `=2.0 xx 10^(-5)//^(@)C, steel = 1.2 xx 10^(-5)//^(@)C`

Explanation

`DeltaL _("steel") = L alpha_("steel") Delta T " " …. (1)`
`Delta L _("Brass") = L alpha_("Brass") Delta T " " … (2)`
Net change in length = `Delta L_("steel") + Delta L_("Brass")`
`= L (alpha_("steel") + alpha_("Brass")) Delta T`
` = 50 (1.2 xx 10^(-5) + 2.1 xx 10^(-5)) (250 - 40)`
`= 0.346` cm