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A metallic wire of length and diameter 3...

A metallic wire of length and diameter 3 m and 0.001 m respectively is stretched by a load of 10 kg.Young's modulus and Poisson's ratio of the material of the wire are respectively `20 times 10^10 N.m^-2` and 0.28 . Calculate the decrease in the diameter of the wire. (`g=9.8 m.s^-2`)

Text Solution

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Young.s modulus, `Y=(F.L)/(A.l)`
or, `l/L=F/(YA)=(10^6times9.8times4)/(20times10^10times3.14times(0.001)^2)[F=10 times9.8 N]`
Again , `sigma=d/D.L/l`
or,`d=(sigmaDl)/L=0.26times0.001times(10times9.8times4)/(20times10^10times3.14times(0.001)^2)`
`=16.23 times 10^-8 m`.
`therefore` Decrease in the diameter of the wire=`16.23 times 10^-8 m`.
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