If the ratio of lengths, radii and Young's moduli of steel and brass wires in the figure are $a, b$ and $c$ respectively, then the corresponding ratio of increase in their lengths is :

Question

If the ratio of lengths, radii and Young's moduli of steel and brass wires in the figure are a , b and c respectively, then the corresponding ratio of increase in their lengths is :

TestHub · Accepted Answer

According to questions, ​ ℓ b ​ ℓ s ​ ​ = a , r b ​ r s ​ ​ = b , y b ​ y s ​ ​ = c , Δ ℓ b ​ Δ ℓ s ​ = ? As, y = A Δ ℓ F ℓ ​ ⇒ Δ ℓ = Ay F ℓ ​ Δ ℓ s ​ = π r s 2 ​ ⋅ y s ​ 3 mg ℓ s ​ ​ [ ∵ F s ​ = ( M + 2 M ) g ] Δ ℓ b ​ = π r b 2 ​ ⋅ y b ​ 2 Mg ℓ b ​ ​ [ ∵ F b ​ = 2 Mg ] ​ ∴ Δ ℓ b ​ Δ ℓ s ​ ​ = π r b 2 ​ ⋅ y b ​ 2 Mg ⋅ ℓ b ​ ​ π r s 2 ​ ⋅ y s ​ 3 Mg ℓ s ​ ​ ​ = 2 b 2 C 3 a ​

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