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 s.

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

Answer 1

Answer: (C)

$\frac{2\sigma T}{AY}$

Answer 2

$\frac{\Delta r}{r} = \sigma\frac{\Delta l}{l}$ and $\frac{\Delta l}{l} = \frac{T}{AY}$

$\frac{\Delta A}{A} = \frac{2\Delta r}{r} = \frac{2\sigma T}{AY}$.