Mechanical Properties Of Solids Question 4
Question 4 - 30 January - Shift 1
Choose the correct relationship between Poisson ratio $(\sigma)$. bulk modulus $(K)$ and modulus of rigidity $(\eta)$ of a given solid object:
(1) $\sigma=\frac{3 K-2 \eta}{6 K+2 \eta}$
(2) $\sigma=\frac{6 K+2 \eta}{3 K-2 \eta}$
(3) $\sigma=\frac{3 K+2 \eta}{6 K+2 \eta}$
(4) $\sigma=\frac{6 K-2 \eta}{3 K-2 \eta}$
Show Answer
Answer: (1)
Solution:
Formula: Relations Between Elastic Constants
$Y=3 \eta(1+\sigma)$
$Y=3 K(1-\sigma)$
$\Rightarrow 2 \eta(1+\sigma)=3 K(1-2 \sigma)$
$\Rightarrow \sigma=(\frac{3 K-2 \eta}{6 K+2 \eta})$
