Question

For a given material young’s modulus is 1 X 105 N/MM2 and modulus of rigidity 0.4 x 105 N/MM2. and poisson’s ratio as 0.25 then value of bulk modulus is​

Answer 1

Answer:

The relation between modulus of elasticity and modulus of rigidity E=2G\left ( 1+\mu \right ) N/m2 or pascal(Pa)

The relation between Young's modulus and bulk modulus E=3K\left ( 1-2\mu \right ) N/m2 or pascal(Pa)

Answer 2

Given:

Young's modulus = $1$ × $10^{5} N/mm^{2}$

Modulus of rigidity = $0.4$ × $10^{5}N/mm^{2}$

Poisson's ratio $=0.25$

To find:

The value of Bulk Modulus.

Explanation:

• Young's modulus is the ratio of stress applied on an object to the strain produced in the object.

• Poisson's ratio is a mathematical abbreviation for the directional deformity produced in an object.

• Bulk modulus is the same value as young's modulus when the load applying stress is a quantity measured as mass or in kilogram.

• The relation between Young's modulus (Y), the Bulk modulus (K) and the Poisson's ratio (μ) is given by

                                  $K=\frac{Y}{3(1-\frac{1}{u} )}$

Solution:

Substituting the given values in the equation above, we get

$K=\frac{1*10^{5} }{3(1-\frac{1}{O.25} )}$

$K=\frac{10^{5} }{3(1-4)}$

$K=\frac{10^{5} }{-9}$

$K=-0.12$ × $10^{5} Pa$

Final answer:

Hence, the value of Bulk modulus is $-0.12Pa$.