First slide

Stress and strain

Question

A metal rod is subjected to tensile force and longitudinal strain produced in the rod is 0.02. If Poisson’s ratio of the metal is 0.3, the change produced in its volume is

Moderate

A

0.3%
B

0.8%
C

0.6%
D

0.9%

Solution

$\begin{array}{l} V = π r^{2} l \\ ∴ \frac{Δ V}{V} = 2 (\frac{Δ r}{r}) + \frac{Δ l}{l} \end{array}$
$B u t \frac{Δ r}{r} = - σ \times \frac{Δ l}{l}$
$\begin{array}{l} ∴ \frac{Δ V \times 100}{V} = (1 - 2 σ) \times \frac{Δ l}{l} \times 100 % \\ = (1 - 2 \times 0 .3) \times 0 .02 \times 100 % = 0 .8 % \end{array}$

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