Two steel wires of same length but radii r and 2r are connected together end to end and tied to a wall as shown. The force stretches the combination by 10 mm. How far (in mm) does the midpoint A move?

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Same tension in both wires: Δ ℓ 1 ​ = A 1 ​ Y F ℓ ​ and Δ ℓ 2 ​ = 4 A 1 ​ Y F ℓ ​ Δ ℓ 1 ​ + Δ ℓ 2 ​ = 10 mm gives Δ ℓ 1 ​ = 8 mm Midpoint A moves by the elongation of the first wire Answer 8.00

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