A brass rod of length 50 cm 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. Coefficient of linear expansion of brass `= 2.0 xx 10^(-5).^(@)C^(-1)` and that of steel `=1.2 xx 10^(-5).^(@)C^(-1)`.

Explanation

Since the ends of the combined rod are not clamped, each rod expands freely.
`Delta l_("brass ") = 0.21 cm, Delta l_("steel") = 0.126 cm = 0.13 cm`
Total change in length ` = 0.34` cm. No .thermal stress. is developed at the junction since the rods freely expand.