Question

A copper wire of cross-section A is under a tension T. Find the decrease in the cross-section area. Young's modulus is Y and Poisson's ratio is $\sigma$

• A. $\frac{\sigma T}{2AY}$
• B. $\frac{\sigma T}{AY}$
• C. $\frac{2\sigma T}{AY}$
• D. $\frac{4\sigma T}{AY}$

Answer 1

The correct option is C $\frac{2\sigma T}{AY}$

$\frac{\Delta d}{d}=-\sigma \frac{\Delta l}{l}=-\sigma \frac{T}{AY}Thus\Delta d=-\sigma d\frac{T}{AY},hence\Delta A=\Delta \left(\pi /4d^2\right)=2.\pi /4.d\Delta dHence\Delta A=2.\pi /4.d.d.\left(\frac{-\sigma T}{AY}\right)=2\frac{-\sigma T}{Y}orDecrease=-\frac{\Delta A}{A}=\frac{2\sigma T}{AY}$