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 are a by 2%. The percentage increases in its length is

Options

A. 0.03
B. 0.025
C. 0.01
D. 0.005

Answer

b

Explanation

Poisson,s ratio, `sigma = 0.4 = (d)/((Delta I)/(I))`
`:'` Area, `A = (pi d^(2))/(4)`
`:.del A = (pi. 2d)/(4) del d`
`:. (del A)/(A) = (2 del d)/(d)`
Given `(Delta A)/(A) xx 100 = 2% = 2 = 2 (Delta d)/(d)`
or `(Delta d)/(d) = 1%`
`:' (Delta d)/(d) = 0.4 (Delta I)/(I) implies (Delta I)/(I) = (1)/(0.4) (Delta d)/(d)`
`= 2.5 xx 1% = 2.5%`