Two wires A and B are made of same material having ratio of lengths L B L A = 3 1 and their diameters ratio d B d A = 2 . If both the wires are stretched using same force, what would be

Question

Two wires A and B are made of same material having ratio of lengths L B ​ L A ​ ​ = 3 1 ​ and their diameters ratio d B ​ d A ​ ​ = 2 . If both the wires are stretched using same force, what would be the ratio of their respective elongations?

TestHub · Accepted Answer

L B ​ L A ​ ​ = 3 1 ​ and d B ​ d A ​ ​ = 2 Δ L A ​ = A A ​ Y A ​ F A ​ L A ​ ​ and Δ L B ​ = A B ​ Y B ​ F B ​ L B ​ ​ Given, F A ​ = F B ​ and Y A ​ = Y B ​ Δ L B ​ Δ L A ​ ​ = A B ​ Y B ​ F B ​ L B ​ ​ A A ​ Y A ​ F A ​ L A ​ ​ ​ = ( L B ​ L A ​ ​ ) ( A A ​ A B ​ ​ ) Δ L B ​ Δ L A ​ ​ = ( L B ​ L A ​ ​ ) ( 4 π ​ d A 2 ​ 4 π ​ d B 2 ​ ​ ) = ( L B ​ L A ​ ​ ) ( d A ​ d B ​ ​ ) 2 Δ L B ​ Δ L A ​ ​ = ( 3 1 ​ ) ( 2 1 ​ ) 2 = 12 1 ​

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