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

F

4F

9F

6F

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Solution

calligraphic l subscript 1 space equals space 3 calligraphic l subscript 2 straight Y space equals space straight F over straight A space straight x fraction numerator calligraphic l subscript 1 over denominator increment straight x end fraction space..... space left parenthesis straight i right parenthesis straight Y space equals fraction numerator straight F apostrophe over denominator straight A end fraction space straight x space fraction numerator calligraphic l subscript 1 divided by 3 over denominator increment straight x end fraction space..... space left parenthesis ii right parenthesis from space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis space we space get straight F over straight A space straight x fraction numerator calligraphic l subscript 1 over denominator increment straight x end fraction space equals space fraction numerator straight F apostrophe over denominator 3 straight A end fraction space straight x fraction numerator calligraphic l subscript 1 over denominator 3 increment straight x end fraction straight F apostrophe space equals space 9 straight F

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