The Poisson's ratio of a material is 0.4. If a force is applied to a wire of this material, there is a decrease of cross-sectional area by 2%. The percentage increase in its length is

Options

A. `3%`
B. `2.5%`
C. `1%`
D. `0.5%`

Answer

C

Explanation

CD = 2x
implies rate of change of length `CD=2(dx)/(dt)=6implies (dx)/(dt)=3m//s`
`implies V_(AX)=3m//s`
`because` length of AD should be constant
`V_(D)` along length `= V_(A)` along length.
`O=V_(AX)xxcos37-V_(AY)cos53`
`V_(AX)((4)/(5))=V_(AY)((3)/(5))=V_(AY)=4m//simplies V_(A)=sqrt(V_(AY)^(2)+V_(AX)^(2))=5m//s`