For a certain solid isotropic material, the modulus of rigidity is found to be 75 % of its bulk modulus. The Poisson's ratio of this material is:

Step-by-step solution

Let the bulk modulus be K and the modulus of rigidity be . Given that = 0.75 K = 3 4 K . The standard relation connecting Poisson's ratio , bulk modulus K , and modulus of rigidity is: = 3K - 2 6K + 2 Substitute = 0.75 K into the formula: = 3K - 2(0.75 K) 6K + 2(0.75 K) = 3K - 1.5K 6K + 1.5K = 1.5K 7.5K = 1.5 7.5 = 1 5 = 0.2 Alternatively, using the relations Y = 3K(1 - 2 ) and Y = 2 (1 + ) : 3K(1 - 2 ) = 2(0.75 K)(1 + ) 3(1 - 2 ) = 1.5(1 + ) 2(1 - 2 ) = 1 + 2 - 4 = 1 + 5 = 1 = 0.2 Answer: 0.2