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Calculate the percentage increase in len...

Calculate the percentage increase in length of a wire of diameter 0.40 mm, stretched by a load of 5 kg. (Given: Young's modulus of elasticity of material of the wire `12.5xx10^(10)Nm^(-2))`

Text Solution

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Given `Y=12.5xx10^(10)Nm^(-2)`
`d=0.4xx10^(-3)m`, Mass `=5kg`
load `=5xx9.8N=49.0N`
Area of cross section of the wire `=(pid^(2))/4`
i.e. `A=(3.142xx(0.4)^(2)xx10^(-6))/4=0.12568xx10^(-6)m^(2)`
We know that `Y=(mgL)/(ADeltaL)`
`:.` Percentage increase in length `=(DeltaL)/Lxx100=(mg)/(YA)xx100`
`=(5xx9.8xx100)/(12.5xx10^(10)xx0.12568xx10^(-6))%=3.119xx10^(-5)%`
`=0.312%`
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