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A copper wire and a steel wire of radii ...

A copper wire and a steel wire of radii in the ratio 1:2, lengths in the ratio 2:1 are stretched by the same force. If the Young's modulus of copper = `1.1 xx 10^11Nm^(-2)` find the ratio of their extensions (young's modulus of steel `= 2 xx 10^11 N//m^2)` .

Text Solution

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we know
`e=(FL)/(pi r^(2)Y) rArr (e_(1))/(e_(2))=((L_(1))/(L_(2))) ((r_(2))/(r_(1)))^(2)((Y_(2))/(Y_(1)))((F)/(F))`
Here `r_(1):r_(2)=1:2, L_(1):L_(2)=2:1, Y_(1)=1.1xx10^(11)Nm^(-2)`,
`Y_(2)=2.0xx10^(11)Nm^(-2)`
`(e_(1))/(e_(2))=(2)/(1)((2)/(1))^(2)((2.0xx10^(11))/(1.1xx10^(11)))=(16)/(1.1)=(160)/(11)`
`e_(1):e_(2)=160:11`
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