The coefficient of linear expansion of brass and steel rods are ₁ and ₂ respectively. Lengths of brass and steel rods are l₁ and l₂ respectively. If (l₂-l₁ ) is maintained same at all temperatures, which one of the following relations is correct?

Step-by-step solution

The correct option is (D). Concept: Length of a metalic rod at a given temperature is given by, l=l₀(1+ T) where, l₀ is the initial length, the coefficient of linear expansion and T the temperature change. At any given temperature the lengths of the brass and steel rods can be written as, l_b=l₁ (1+ ₁ T ) and l_s=l₂ (1+ ₂ T ) respectively. Therefore, at difference of length is given by, aligned & l_b-l_s=l₁ (1+ ₁ T )-l₂ (1+ ₂ T ) & l_b-l_s= (l₁-l₂ )+ ( ₁ l₁-l₂ ₂ ) T aligned Since, l_b-l_ s =l₁-l₂ as the difference