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An aluminium wire 1 m in length and radi...

An aluminium wire 1 m in length and radius 1 mm is loaded with a mass of 40 kg hanging vertically. Young’s modulus of Al is `7.0 xx 10^(10) N//m^(2)`. Calculate (a) tensile stress (b) change in length (c) tensile strain and (d) the force constant of such a wire.

Text Solution

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(a) Stress = `(F)/(A)=(mg)/(pir^(2))=(40xx10)/(pixx(1xx10^(-3))^(2))=1.27xx10^(8)N/m^(2)`
(b) `DeltaL=(FL)/(AY)=(40xx10xx1)/(pixx(1xx10^(-3))^(2)xx7xx10^(10))=1.8xx10^(-3)` m
(c) Strain `=(DeltaL)/(L)=(1.8xx10^(-3))/(1)=1.8xx10^(-3)`
(d) F=Kx=K`Delta`L,K = Force constant
`K=(DeltaF)/(L)=(40xx10)/(1.8xx10^(-3)=2.2xx10^(5)N/m`
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