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A copper wire and an aluminium wire have...

A copper wire and an aluminium wire have lengths in the ratio `3:2,` diameters in the ratio `4:3,`Forces in the ratio `4:5.` Find the ratio of increase in length of the two wires. `(Y_(cu)=1.1xx10^(11)N//m^(-2),Y_(AI)=0.7xx10^(11)Nm^(-2)`

Text Solution

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Ratio of Lengths,`l_(1):l_(2)=3:2,`
Ratio of diameters, `d_(1):d_(2)=2:3`
Ratio of forces, `F_(1):F_(2)=4:5`
`Y_(1)=Y"of copper"=1.1xx10^(11)`
`Y_(2)=Y"of Aluminium"=0.7xx10^(11),`
Ratio of elongation, `e_(1):e_(2)=?`
`e=(Fl)/(AY)=(4Fl)/(pid^(2)Y)therefore(e_(1))/(e_(2))=(4F_(1)l_(1))/(pid_(1)^(2)Y_(1))xx(pid_(2)^(2)Y_(2))/(4F_(2)l_(2))`
`rArr(e_(1))/(e_(2))=(F_(1)l_(1)d_(2)^(2)Y_(2))/(F_(2)l_(2)d_(1)^(2)Y_(1))=(3xx3xx3^(2)xx0.7xx10^(11))/(5xx2xx2^(2)xx1.1xx10^(11))`
`=(189)/(110)thereforee_(1):e_(2)=189:110`
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