Discussion
The ratio of Young's modulus to the modulus of rigidity of a material with Poisson's ratio 0.2 will be ______.
Answer: B
The elastic constants are connected by \(E = 2G(1 + \nu)\), where E is Young's modulus, G the modulus of rigidity and \(\nu\) Poisson's ratio. So
\[ \frac{E}{G} = 2(1 + \nu) = 2(1 + 0.2) = 2.4 \]The value 0.2 is just Poisson's ratio. The values 2.8 and 3.2 would come from using a Poisson's ratio of 0.4 or 0.6 and are not consistent with the data. The ratio of E to G for any real material lies between 2 and 3.
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