Question

The values of Y, ɳ and K (Young’s modulus, coefficient of rigidity and Bulk
Modulus) for brass is 90× 109
, 35× 109
and 75× 109
respectively. The Poisson’s ratio
will be

Answer 1

The Poisson's ratio is 0.3

Explanation:

Given:

Young's Modulus $Y=9\times 10^9$ Pa

Coefficient of rigidity $\eta=3.5\times 10^9$ Pa

Bulk Modulus $K=7.5\times 10^9$ Pa

To find out:

The Poisson's ratio

Solution:

The relation between Young's Modulus (Y), Bulk Modulus (K) and Poisson's ratio (ν) is given by

$Y=3K(1-2\nu)$

$\implies 9\times 10^9=3\times 7.5\times 10^9(1-2\nu)$

$\implies 3=7.5(1-2\nu)$

$\implies 1-2\nu=\frac{3}{7.5}$

$\implies 2\nu=1-\frac{3}{7.5}$

$\implies 2\nu=\frac{4.5}{7.5}$

$\implies \nu=\frac{45}{75\times 2}$

$\implies \nu=0.3$

Hope this answer is helpful.

Know More:

Q: If young's modulus of elasticity Y for a material is one and half times its rigidity coefficient G , the Poisson's ratio will be:

Click Here: https://brainly.in/question/12061808