Two rods one of aluminium of length ℓ 1 having coefficient of linear expansion α a , and other steel of length ℓ 2 having coefficient of linear expansion α s are joined end to end. The expansi

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Two rods one of aluminium of length ℓ 1 ​ having coefficient of linear expansion α a ​ , and other steel of length ℓ 2 ​ having coefficient of linear expansion α s ​ are joined end to end. The expansion in both the rods is same on variation of temperature. Then the value of ℓ 1 ​ + ℓ 2 ​ ℓ 1 ​ ​ is:

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Equal expansion: ℓ 1 ​ α a ​ Δ T = ℓ 2 ​ α s ​ Δ T ⇒ ℓ 1 ​ ℓ 2 ​ ​ = α s ​ α a ​ ​ ℓ 1 ​ + ℓ 2 ​ ℓ 1 ​ ​ = 1 + ℓ 2 ​ / ℓ 1 ​ 1 ​ = 1 + α a ​ / α s ​ 1 ​ = α a ​ + α s ​ α s ​ ​ Option (A).

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