Two rods of different metals of coefficient of linear expansion alpha_(1) and alpha_(2)and initial length l_(1) and l_(2) respectively are heated to the same temperature. Find relation in alpha_(1), alpha_(2), l_(1) and l_(2 )such that difference between their lengths remain constant.

Two rods of different metals of coefficient of linear expansion alpha_

1.	Two rods of different metals of coefficient of linear expansion alpha_(1) and alpha_(2)and initial length l_(1) and l_(2) respectively are heated to the same temperature. Find relation in alpha_(1), alpha_(2), l_(1) and l_(2 )such that difference between their lengths remain constant.
Answer» Solution :`I_(1)^(1)=I_(1)[1+alpha_(1)(t_(2)-t_(1))]` `I_(2)^(1)=I^(1)[1+alpha_(2)(t_(2)-t_(1))]` GIVEN that the difference in their length remain CONSTANT `:. I_(2)^(1)-_(1)^(1)=I_(2)-_(1)` `I_(2)[1+alpha_(2)(t_(1)-t_(2))]-I_(1)[1+alpha_(1)(t_(2)-t_(1))]=I_(2)-I_(1)` `:. I_(2)alpha_(2)=I_(1)alpha_(1)`