A uniform cylindrical wire is subjected to a longitudinal tensile stress of `5 xx 10^(7) N//m^(2)`. Young's modulus of the material of the wire is `2 xx 10^(11) N//m^(2)`. The volume change in the wire is `0.02%`. The factional change in the radius is

Options

A. `0.25xx10^(-4)`
B. `0.5xx10^(-4)`
C. `1.0xx10^(-4)`
D. `1.5xx10^(-4)`

Answer

A

Explanation

`Y="Stress"/(/_\L//L)` or `(/_\L)/L="stress"/Y=(5x10^(7))/(2xx10^(11))=2.5xx10^(-4)`
Now `V=pir^(2)L`
`(/_\V)/V=(pi/_\(r^(2)L))/(pir^(2)l)`
or `(/_\V)/V=(r^(2)/_\L+Lxxpi/_\r)/(r^(2)L)` or `(/_\L)/V=(/_\V)/V=(/_\L)/L+2(/_\r)/r`
or `(/_\V)/r=(/_\V)/V-(/_\L)/L` or `2 (/_\r)/r=0.02/100 xx100^(-4)=-0.25xx10^(-4)`