Coefficient of linear expansion of brass and steel rods are α1and α2 . Length of brass and steel rods are l1 and l2 respectively. If l2–l1 is maintained same at all temperatures, then find the ratio of α1 to α2.
A
l2l1
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B
l1l2
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C
α2l1
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D
l2α1
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Solution
The correct option is Al2l1 Let l1 and l2 be length of the rods at temperature T. For any temperature t, length of rods can be given as l1′=l1(1+α1ΔT) l2′=l2(1+α2ΔT) Given: l2′−l1′= constant l2(1+α2ΔT)−l1(1+α1ΔT)=constant l2(1+α2×(t−T))−l1(1+α1×(t−T))=constant Differetiating both side w.r.t. t l2α2=l1α1 i.e α1α2=l2l1