A rod of length 20 cm is made of metal. It expands by 0.075 cm when its temperature is raised from the 0o C to 100o C. Another rod of a different metal B having the same length expand by 0.045 cm for the same change in temperature. A third rod of the same length is composed of two parts, one of metal A and the other of metal B. This rod expands by 0.060 cm for the same change in temperatures. What is the length of he portion made of metal A ?

As we know that, solid when expanded in one dimension (linear expansion) follows the following equation:l=lo(1+αΔT)where ΔT is the change in temperature to cause the expansion. Expanding the above equation, we can get:l−lo=loαΔT⇒Δl=loαΔT⇒α=ΔlloΔTFollowing figure depicts the situation as given:In rod A,0.075=20×αA×100αA=752×10−6/∘CIn rod B,0.045=20×αB×100αB=452×10−6/9CNow the overall increase in the given rod would be the sum of both rod A and rod⁡ B.⇒0.060=x×αA×ΔT+(20−x)×αB×ΔT⇒0.060=x×752×10−6×100+20-x×452×10-6×100⇒x=10cm