A copper wire of cross sectional asrea 0.01 cm is under a tension of 20 N. Find the decrease in the cross sectional area. Young modulus of copper `=1.1xx10^11Nm^-2` and Poisson ratio 0.32.

Explanation

Given, tension `= 20N`
area of cross section `= 0.01cm^(2) = 1xx10^(-6) m^(2)`
Young's Modulus, `Y = 1.1xx10^(11) N//m^(2)`
`F = (YA Delta l)/(l) rArr (Delta l)/(l) = (F)/(YA)`
`= (20)/(1.1xx10^(11)xx10^(-6)) = (20)/(11) xx 10^(-4)N`,
From poisson's ratio
`(Delta r)/(r) = sigma xx (Delta l)/(l) = 0.32 xx (20)/(11) xx 10^(-4)`
area of the wire is
`A = pi r^(2), A alpha r^(2), (Delta A)/(A) = 2xx (Delta r)/(r)`
`(Delta A)/(A) = 2xx0.32 xx (20)/(11) xx 10^(-4) = 1.16xx10^(-4) m^(2)`
Decreases in cross sectional area of the wire is
`Delta A = 1.16xx10^(-4) xx 10^(-6) = 1.16xx10^(-10) m^(2)`