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Question: Given the following values for an elastic material Young's modulus = 7 × 10<sup>10</sup> Nm<sup>–2</...

Given the following values for an elastic material Young's modulus = 7 × 1010 Nm–2 and Bulk modulus = 11 × 1010 Nm–2. The Poisson's ratio of the material is –

A

0.12

B

0.24

C

0.31

D

0.39

Answer

0.39

Explanation

Solution

K = Y3(12σ)\frac{Y}{3(1 - 2\sigma)} or 11 × 1010 = 7×10103(12σ)\frac{7 \times 10^{10}}{3(1 - 2\sigma)}

or 733\frac{7}{33} = 1– 2s or 2s = 1 – 733\frac{7}{33}

s = 2633\frac{26}{33} = 0.39