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An aluminium wire and a steel wire of th...

An aluminium wire and a steel wire of the same length and cross-section are joined end- to-end. The composite wire is hung from a rigid support and a load is suspen-ded from the free end. If the increase in lengthe of the composite wire is 1.35 mm, find the ratio the (i) stress in the two wires amd (ii) strain in the two wires.
`(Y_(Al)=0.7xx10^(!1)Nm^(-2),Y_("steel")=2=10^(11)Nm^(-2))`

Text Solution

Verified by Experts

i. Length is same`rArrl_(1)=l_(2)`
Area is same`A_(1)=A_(2)`
In composite wire same load will act on
both wires.
`therefore"Ratio of stress"=1:1`
`"ii. Total elongation,"e=1.35mm=e_(Al)+e_(s)`
`"Young.s modulus of aluminium"=7xx10^(10)`
`N//m^(2),`
`"Y of steel"=2xx10^(11)N//m^(2)`
`"Elongation, e"=(Fl)/(AY)`
But F, l A are same
`thereforeeprop(1)/(Y)or(e_(Al))/(e_(s))=(Y_(s))/(U_(Al))=(20xx10^(10))/(7xx10^(10))=(20)/(7)`
`therefore"Ratio of strain in the wires is"20:7.`
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