In a particular material, if the modulus of rigidity is equal to the bulk modulus then the Poisson’s ratio will be  

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WBMSC Sub-Assistant Engineer (Civil) 05 Jun 2022 Official Paper
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  1. 1
  2. \(\frac{1}{2}\)
  3. \(\frac{1}{4}\)
  4. \(\frac{1}{8}\)

Answer (Detailed Solution Below)

Option 4 : \(\frac{1}{8}\)
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Detailed Solution

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Concept:

We know,

Relation between E, K and ν

E = 2G (1 + μ )  -- (1)

E = 3K (1 - 2μ)  --- (2)

Where, Bulk modulus (K), Young’s modulus (E), and Poisson’s ratio (μ) 

G - Modulus of rigidity

Calculation:

Given, K = G

From (1) & (2)

2G (1 + μ ) = 3K (1 - 2μ)

2G (1 + μ ) = 3G (1 - 2μ) 

 2 + 2μ = 3 - 6μ 

8μ = 1

∴ μ = 1/8

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