Question

A uniform cylindrical wire is subjected to a longitudinal tensile stress of $5\times {10}^{7}N/m^2$. Young’s modulus of the material of the wire is $2\times {10}^{11}N/m^2$. The volume change in the wire is $0.02\%$. The magnitude of fractional change in the radius is

• A. $0.25\times {10}^{-4}$
• B. $0.5\times {10}^{-4}$
• C. $1.0\times {10}^{-4}$
• D. $1.5\times {10}^{-4}$

Answer 1

The correct option is A $0.25\times {10}^{-4}$

$\frac{\Delta V}{V}=2\times {10}^{-4}$
$\frac{\Delta L}{L}=\frac{Stress}{Y}=\frac{5\times {10}^7}{2\times {10}^{11}}$ = $2.5\times {10}^{-4}$
$V=\pi r^{2}L$
Taking log both side, we get
$\frac{\Delta V}{V}=2\frac{\Delta r}{r}+\frac{\Delta L}{L}$
If we substitute the values in (1) we get
$\frac{\Delta r}{r}=0.25\times {10}^{-4}$