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 fractional change in the radius is

Options

A. `0.25xx10^-4`
B. `0.5cc10^-4`
C. `1.0xx10^-4`
D. `1.5xx10^-4`

Answer

A

Explanation

`Y=(stress)/((triangleL)/(L))` or `(triangleL)/(L)=(stress)/(Y)=(5xx10^7)/(2xx10^(11))=2.5xx10^-4`
Now, `V=pir^2L`
`(triangleV)/(V)=(pitriangle(r^2L))/(pir^2L)`
or `(triangleV)/(V)=(r^2triangleL+Lxx2rtriangler)/(r^2L)`
or `(triangleL)/(V)=(triangleL)/(L)+2(triangler)/( r)
or `2(triangler)/(r )=(triangleV)/(V)-(triangleL)/(L)`
or `2(triangler)/( r)=(0.02)/(100)-2.5xx10^-4`
or `(triangler)/( r)=1xx10^-4-(2.5)/(2)xx100^-4=-0.25xx10^-4`