Two wires are made of the same material and have the same volume. However wire 1 has crosssectional area A and wire-2 has cross-sectional area 3 A . If the length of wire 1 increases by Δ x on applyin

Question

Two wires are made of the same material and have the same volume. However wire 1 has crosssectional area A and wire-2 has cross-sectional area 3 A . If the length of wire 1 increases by Δ x on applying force F , how much force is needed to stretch wire 2 by the same amount?

TestHub · Accepted Answer

​ A 1 ​ ℓ 1 ​ = A 2 ​ ℓ 2 ​ ⇒ ℓ 2 ​ = A 2 ​ A 1 ​ ℓ 1 ​ ​ = 3 A A × ℓ 1 ​ ​ = 3 ℓ 1 ​ ​ ⇒ ℓ 2 ​ ℓ 1 ​ ​ = 3 Δ x 1 ​ = A γ F 1 ​ ​ × ℓ 1 ​ Δ x 2 ​ = 3 A γ F 2 ​ ​ ℓ 2 ​ Here Δ x 1 ​ = Δ x 2 ​ 3 A γ F 2 ​ ​ ℓ 2 ​ = A γ F 1 ​ ​ ℓ 1 ​ F 2 ​ = 3 F 1 ​ × ℓ 2 ​ ℓ 1 ​ ​ = 3 F 1 ​ × 3 = i ) ​

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