Question

Choose the correct relationship between Poisson ratio $(\sigma)$, bulk modulus $( K )$ and modulus of rigidity $(\eta)$ of a given solid object :

• A. $\sigma=\frac{3 K+2 \eta}{6 K+2 \eta}$
• B. $\sigma=\frac{6 K-2 \eta}{3 K-2 \eta}$
• C. $\sigma=\frac{3 K-2 \eta}{6 K+2 \eta}$
• D. $\sigma=\frac{6 K+2 \eta}{3 K-2 \eta}$

Answer 1

Answer: (C)

$\sigma=\frac{3 K-2 \eta}{6 K+2 \eta}$

Answer 2

The correct answer is (C) : $\sigma=\frac{3 K-2 \eta}{6 K+2 \eta}$
Y=3η(1+σ)
Y=3K(1−σ)
⇒2η(1+σ)=3K(1−2σ)
⇒σ=(6K+2η3K−2η​)