A tension of 22N is applied to copper wire of crosssectional area `0.02cm^2`,Young's modulus of copper is `1.1xx10^11N/m^2` and poisson's ratio 0.32.The decrease in cross-sectional area will be

Options

A. `1.28xx10^-6 cm^2`
B. `1.6xx10^-6 cm^2`
C. `2.56xx10^-6 cm^2`
D. `0.64xx10^-6 cm^2`

Answer

A

Explanation

strain,
`(Deltal)/l =F/(DeltaE)=22/(0.02xx10^(-4)xx1.1xx10^(11))=10^(-4)`
poisson's ratio,
`sigma=((Deltar)/r)/((Deltal)/l)`
`therefore (Deltar)/r =sigmaxx(Deltal)/l = 0.32xx10^(-4)=3.2xx10^(-5)`
Change in cross sectional area,
`Delta A=2 (Deltar)/r xx A=2xx0.32 xx 10^(-4)xx0.02xx10^(-4)=1.28 xx 10^(-10)m^(2)=1.28 xx 10^(-6)cm^(2)`.