Question

The increase in the length of a wire on stretching is $0.025\%$. If its Poisson's ratio is $0.4$, then the percentage decrease in the diameter is :

• A. $0.01$
• B. $0.02$
• C. $0.03$
• D. $0.04$

Answer 1

The correct option is A $0.01$

Suppose, D be the diameter of the wire Poissons ratio,

$\sigma =\frac{lateralstrain}{longitudinalstrain}$

$\sigma =\frac{\frac{\Delta D}{D}}{\frac{\Delta L}{L}}$

$\frac{\Delta L}{L}=0.025$

$\sigma =0.004$

$\sigma =\frac{\frac{\Delta D}{D}}{\frac{1}{40}}$

$\frac{\Delta D}{D}=\frac{1}{40}\times 0.4=0.01$