A material has Poisson ratio `0.5`. If a rod of material has a longitudinal strain `2xx10^-3`, the percentage change in volume is :

Options

A. 0.6
B. 0.4
C. 0.2
D. zero

Answer

D

Explanation

Here poisson's ratio`=((triangler)/( r))/((trianglel)/(l))`
In this case `(trianglel)/(l)=2xx10^-3` and `sigma=0.5`
`(triangler)/(r )=sigma(trianglel)/(l)`
`=2xx10^-3xx5.0=10^-3`
Let V be the initial volume and `(V+triangleV)` be the final volume then
`V=pir^2l`
`V+triangleV=pi(r-triangler)^2(l-trianglel)`
`triangleV=pir^2trianglel-2pirltriangler`
(subtracting and simplifying)
`(triangleV)/(V)=(trianglel)/(l)-(2triangler)/(r )`
`=2xx10^-3-2xx10^-3=0`
Correct choice is (d).