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

Question

Two wires are made of two different material and have the same volume. However wire 1 has cross-sectional area A and wire 2 has cross-sectional area 3A. If the length of each wire increases by Δ x on applying force F , then find ratio of their young's modulus.

TestHub · Accepted Answer

Same volume: A 1 ​ L 1 ​ = A 2 ​ L 2 ​ ⇒ L = A V ​ Young's modulus: Y = A Δ x F L ​ = A 2 Δ x F V ​ F, V and Δx are the same for both wires, so Y 2 ​ Y 1 ​ ​ = ( A 1 ​ A 2 ​ ​ ) 2 = ( A 3 A ​ ) 2 = 9 Answer: 9

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