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

$Y=3 \eta(1+\sigma)$

$Y=3 K(1-\sigma)$

$\Rightarrow 2 \eta(1+\sigma)=3 K(1-2 \sigma)$

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