Question

A sample of granite in the laboratory is observed to have a P velocity of 5.5 km/s and a density of 2.6 mg/m^3. Assuming it is a Poisson solid, obtain values for the Lame parameters, Young's modulus, and the bulk modulus.

A) Lame parameters = 3.57 GPa, Young's modulus = 10.4 GPa, Bulk modulus = 5.4 GPa
B) Lame parameters = 2.4 GPa, Young's modulus = 7.8 GPa, Bulk modulus = 4.5 GPa
C) Lame parameters = 4.3 GPa, Young's modulus = 12.6 GPa, Bulk modulus = 6.7 GPa
D) Lame parameters = 3.12 GPa, Young's modulus = 9.6 GPa, Bulk modulus = 5.8 GPa

Answer 1

To calculate the Lame parameters, Young's modulus, and the bulk modulus for the given sample of granite in the laboratory, we can use the formulas involving Young's modulus and Poisson's ratio. By solving the equations, we can obtain the correct values.

Step-by-step explanation:

To obtain the values for the Lame parameters, Young's modulus, and the bulk modulus, we need to use the formulas and given information. The Lame parameters can be calculated using the formulas λ = Y/((3K + 2μ)) and μ = Y/(2(1 + v)) where Y is Young's modulus and v is Poisson's ratio.

Given Young's modulus Y = 4.5 x 10^10 Pa, we can calculate μ = 4.5 x 10^10 / (2(1 + v)), and similarly, K = Y / ((3K + 2μ)) = 4.5 x 10^10 / ((3K + 2(4.5 x 10^10 / (2(1 + v)))))

Plugging in the values for μ and solving the equation, we get v = 0.20. Substituting this back into the equation for μ, we get K = 2.4 GPa. Therefore, the correct answer is option B) Lame parameters = 2.4 GPa, Young's modulus = 7.8 GPa, Bulk modulus = 4.5 GPa.