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JEE Main202124 Feb 2021Morning ShiftPhysicsMechanical Properties of SolidsActual

If Y , K and η are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.

Options

  1. AY = 9   K η 3   K - η N   m - 2
  2. Bη = 3 Y K 9 K + Y N   m - 2
  3. CK = Y η 9 η - 3 Y   N   m - 2
  4. DY = 9   K η 2 η + 3   K   N   m - 2

Correct answer

C. K = Y η 9 η - 3 Y   N   m - 2

Step-by-step solution

Y - Young's modulus, K - Bulk modulus, η - modulus of rigidity We know that, Y = 3 k 1 - 2 σ ⇒ σ = 1 2 1 - Y 3 k                       . . . 1 ⇒ Y = 2 η 1 + σ ⇒ σ = Y 2 η - 1         . . . 2 From the equation 1 and the equation 2 1 2 1 - Y 3 k = Y 2 η - 1 ⇒ 1 - Y 3 k = Y η - 2 ⇒ Y 3 k = 3 - Y n ⇒ Y 3 k = 3 η - Y η ⇒ η Y 3 k = 3 η -

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