The coefficients of linear expansion of brass and steel rods are α₁ and α₂. The lengths of the brass and steel rods are l₁ and l₂ respectively. If (l₂-l₁) is maintained the same at all temperatures, which one of the following relations holds good?

Question

Accepted Answer

(2) α₁ l₁=α₂ l₂. Given: l₁'=l₁(1+α₁Δ T) and l₂'=l₂(1+α₂Δ T). Idea: the gap between the rods is fixed only if both rods lengthen by the same amount at every temperature rise. l₂'-l₁'=(l₂-l₁)+(l₂α₂-l₁α₁)Δ T For this to equal (l₂-l₁) for every Δ T, the bracket must vanish. l₂α₂-l₁α₁=0 α₁ l₁=α₂ l₂

The coefficients of linear expansion of brass and steel rods are α₁ and α₂. The lengths of the brass and steel rods are l₁ and l₂ respectively. If (l₂-l₁) is maintained the same at all temperatures, which one of the following relations holds good?

Step-by-step solution

Why the other options are wrong