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JEE Main202330 Jan 2023Morning ShiftPhysicsMechanical Properties of SolidsActual

Choose the correct relationship between Poisson ratio σ , bulk modulus ( K ) and modulus of rigidity η of a given solid object:

Options

  1. Aσ = 3 K - 2 η 6 K + 2 η
  2. Bσ = 6 K + 2 η 3 K - 2 η
  3. Cσ = 3 K + 2 η 6 K + 2 η
  4. Dσ = 6 K - 2 η 3 K - 2 η

Correct answer

A. σ = 3 K - 2 η 6 K + 2 η

Step-by-step solution

The relations of Young's modulus, Y , bulk modulus, K , the modulus of rigidity, η and Poisson's ratio, σ are given as Y = 3 K ( 1 - 2 σ )   … 1 and Y = 2 η 1 + σ   … 2 From equation 1   and   2 , we have ⇒ 2 η 1 + σ = 3 K 1 - 2 σ ⇒ σ = 3 K - 2 η 6 K + 2 η

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