Question

A material has modulus of rigidity equal to 0.4x10^5 N/mm2 and Bulk modulus
equal to 0.95 x10^5N/mm2 The Young's modulus value in GPa is..​

Answer 1

Given info : A material has modulus of rigidity equal to 0.4 x 10^5 N/mm² and Bulk modulus

equal to 0.95 x 10^5 N/mm².

To find : The Young's modulus value in GPa is..

solution : we know,

E = 2G(1 + μ). ...(1)

E = 3K(1 - 2μ). ...(2)

from equations (1) and (2),

(E/2G - 1) = (1 - E/3K)/2

⇒(E - 2G)/2G = (3K - E)/6K

using G = modulus of rigidity = 0.4 × 10^5 N/mm²

K = bulk modulus = 0.95 × 10^5 N/mm²

⇒(E - 2 × 0.4 × 10^5)/2 × 0.4 × 10^5 = (3 × 0.95 × 10^5 - E)/6 × 0.95 × 10^5

⇒(E - 0.8 × 10^5) × 5.7 × 10^5 = 0.8 × 10^5(2.85 × 10^5 - E)

⇒(E - 0.8 × 10^5) × 0.7 = (2.85 × 10^5 - E)

⇒0.7E - 0.56 × 10^5 = 2.85 × 10^5 - E

⇒1.7E = 3.41 × 10^5

⇒E ≈ 2 × 10^5 N/mm² = 2 × 10¹¹ N/m²

= 200 GPa

Therefore the Young's modulus value in GPa is 200 (approx).

Answer 2

Answer:

Step-by-step explanation: