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A uniform wire (Y=2xx10^11 N//m^2) is s...

A uniform wire `(Y=2xx10^11 N//m^2)` is subjected to a longitudinal tensile stress of `5xx10^(7) N//m^2`. If the overall volume change in the wire is 0.02% the fractional decrease in its radius is `5kxx10^(-6)` Find the value of k

Text Solution

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Strain=`(Deltal)/l = "stress"/Y=(5xx10^7)/(2xx10^11)=2.5xx10^(-4)`
Volume V=Al
`DeltaV=Adeltal+l DeltaA`
`(DeltaV)/V =(Deltal)/l =(DeltaA)/A`
`rArr 2xx10^(-4)=2.5xx10^(-4)+(DeltaA)/A`
`rArr (DeltaA)/A=0.5xx10^(-4)`
`therefore (DeltaA)/A=(2Deltar)/r`
`|(Deltar)/r|=1/2|(DeltaA)/A|=1/2xx0.5xx10^(-4)=0.25xx10^(-4)`
k=5
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