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

Answer: (B)

l1α1=l2α2

Answer 2

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