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Coefficient of linear expansion of brass and steel rods are α₁ and α₂. 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 holds good?

1. α₁l₂ = α₂l₁
2. α₁l₂ = α₂l₁
3. α₁l₂ = α₂l₁
4. α₁l₁ = α₂l₂

Correct answer: α₁l₁ = α₂l₂

Solution

For the difference in lengths (l₂ − l₁) to remain constant at all temperatures, the thermal expansions of both rods must be equal. This leads to the condition α₁l₁ = α₂l₂.

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