A steel wire having cross-sectional area 2 mm^(2)` is stretched by 20 N. Find the lateral strain produced in the wire

Options

A. `0.1955 xx 10^(-4)`
B. `0.391 xx 10^(-4)`
C. `0.1455 xx 10^(-4)`
D. None of the above

Explanation

Given, `Y_("steel") = 2 xx 10^(11) Nm^(-2), sigma = 0.391`
`A = 2 mm^(2) = 2 xx 10^(-6) m^(2)`
Lateral strain = ?
Longitudianl stress = `(F)/(A) = (20)/(2 xx 10^(-6)) = 10^(7) Nm^(-2)`
Young's modulus (Y) = `("Longitudinal stress")/("Longitudinal strain")`
Longitudinal strain `= ("Longitudinal stress")/(Y)`
` = (10^(7))/(2 xx 10^(11)) = 0.5 xx 10^(-4)`
Poisson's ratio `= ("Laterals strain")/("Longitudinal strain")`
Longitudinal strain `xx` Poisson's ratio = lateral strain
Lateral strain `= sigma xx` longitudinal strain
`= 0.391 xx 0.5 xx 10^(-4) = 0.1955 xx 10^(-4)`