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 ∆l on applying a force F, how much force is needed to stretch the second wire by the same amount?

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 ∆l on applying a force F, how much force is needed to stretch the second wire by the same amount?

Infinity Learn · Accepted Answer

Young's modulus, $$Y=FlA$$ΔlSince initial volume of wires are same Their areas of cross sections are A and $$3$$ A  and lengths are $$3l$$ and l respectively.For wire $$1$$,Δ$$l=FAY3l$$            ...........(i)  For wire $$2$$ , let F' force is applied F'$$3A=Y$$Δll⇒Δ$$l=F$$'$$3AYl$$         ..........(ii)From$$ the equations $$(i) and (ii)Δ$$l=FAY3l=F$$'$$3AYl$$⇒F':

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