Two rods, one of aluminium and the other made of steel, having initial length $$l1$$ and $$l2$$ are connected together to form a single rod of length $$l1+l2$$. The coefficients of linear expansion for aluminium and steel are αa and αs respectively. If the length of each rod increases by the same amount when their temperature are raised by $$t0C$$, then find the ratio $$l1(l1+l2)$$

Question

Two rods, one of aluminium and the other made of steel, having initial length $$l1$$ and $$l2$$ are connected together to form a single rod of length $$l1+l2$$. The coefficients of linear expansion for aluminium and steel are αa and αs respectively. If the length of each rod increases by the same amount when their temperature are raised by $$t0C$$, then find the ratio $$l1(l1+l2)$$

Infinity Learn · Accepted Answer

Given ∆$$l1$$ $$=$$ ∆$$l2$$ or $$l1$$αat $$=$$ $$l2$$α$$stl1l2=$$ αsαa or $$l1l1+l2$$ $$=$$ αsα$$a+$$αs

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