Question

The coefficient of linear expansion of brass and steel rod are ‘α₁’ and ‘α₂’ 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 relation is correct?

• A. α₁l₂ = α₂l₁
• B. l₁α₁=l₂α₂
• C. α₁l₂²=α₂l₁²
• D. α₁²l²=α₂²l₁

Answer 1

The Correct Option is B

Let's consider the relation between the change in length (Δl) and the original length (l) for each rod: 
For the brass rod, we have: 
Δl₁ = α₁ x l₁ x ΔT
For the steel rod, we have: 
Δl₂ = α₂ x l₂ x ΔT 
Here, ΔT represents the change in temperature. 
Given that (l₂ - l₁) is maintained the same at all temperatures, we can equate the changes in length: 
Δl₁ = Δl₂ 
Substituting the expressions for Δl₁ and Δl₂ from above: 
α₁ x l₁ x ΔT = α₂ x l₂ x ΔT 
The ΔT cancels out from both sides, giving us: 
α₁l₁ = α₂l₂ 
Therefore, the correct relation is option (B): l₁α₁ = l₂α₂