If a wire of length 4 m and cross-sectional area of 2 `m^(2)` is stretched by a force of 3 kN, then determine the change in length due to this force, Given, Young's modulus of material of wire is `110 xx 10^(9) Nm^(-2)`

Options

A. `60.2 xx 10^(-3) mm`
B. `54.5 xx 10^(-6) mm`
C. `56.4 xx 10^(-3) mm`
D. `62.5 xx 10^(-3) mm`

Explanation

Given, area of cross-section, `A = 2 m^(2)`
Force, `F = 3 kN = 3 xx 10^(3) N`
Length L = 4m
Young's modules, `Y = 110 xx 10^(9) Nm^(-2)`
Change in length `Delta L = ?`
Apply, `Y = ("Stress")/("Strain") = (F//A)/((Delta L)/(L)) = (FL)/(A Delta L)`
`implies Delta L = (FL)/(AY) = (3 xx 10^(3) xx 4)/(2 xx 110 xx 10^(9))`
`= 0.0545 xx 10^(-6) m = 54.5 xx 10^(-6) mm`