Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by Δl on applying a force F, how much force is needed to stretch the second wire by the same amount?
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Question

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by Δl on applying a force F, how much force is needed to stretch the second wire by the same amount?

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G1 Physics · Accepted Answer

Step 1: For a uniform wire, extension is Δl = FL/(AY). Step 2: Let lengths be L₁ and L₂. Equal volumes imply AL₁ = (3A)L₂, so L₂ = L₁/3. Step 3: For wire 1, Δl = FL₁/(AY). Step 4: For wire 2, Δl = F′L₂/(3AY) = F′L₁/(9AY). Step 5: Equal extensions give FL₁/(AY) = F′L₁/(9AY) ⇒ F′ = 9F. Final answer: (C) 9F.