Question Details

Which of the following relations is true

Options

A

3Y = K(1 – σ)

B

K = 9ηY/(Y + η)

C

σ = (6K + η) Y

D

σ = (0.5Y - η)/ η

Correct Answer :

σ = (0.5Y - η)/ η

Solution :

The correct relation is:
σ=0.5Y-ηη

Step-by-step derivation:
The standard relationship linking Young's modulus (Y), modulus of rigidity (η), and Poisson's ratio (σ) is:
Y=2η(1+σ)

To express this relation in terms of σ, we rearrange the equation:
Divide both sides by 2:
0.5Y=η(1+σ)

Expand the right side of the equation:
0.5Y=η+ησ

Subtract η from both sides:
0.5Y-η=ησ

Divide both sides by η to isolate σ:
σ=0.5Y-ηη

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