The values of Young’s and bulk modulus of elasticity of a material are 8 x 10¹⁰ N /m² and 10 x10¹⁰ N /m² respectively. The value of Poisson’s ratio for the material will be

To find the Poisson's ratio of the material, we can use the fundamental relation between Young's modulus ($E$), Bulk modulus ($K$), and Poisson's ratio ($\sigma$).

The standard relation is given by the formula:
$E=3K(1-2\sigma )$
Where:
• $E$ is the Young's modulus of elasticity.
• $K$ is the Bulk modulus of elasticity.
• $\sigma$ is the Poisson's ratio.

From the question, the given values are:
Young's modulus, $E=8\times {10}^{10}{\text{N/m}}^2$
Bulk modulus, $K=10\times {10}^{10}{\text{N/m}}^2$

Substitute these values into the relation:
$8\times {10}^{10}=3\times (10\times {10}^{10})\times (1-2\sigma )$

We can simplify this equation by dividing both sides by ${10}^{10}$:
$8=30(1-2\sigma )$

Now, solve for $\sigma$:
$1-2\sigma =\frac{8}{30}$
$1-2\sigma =\frac{4}{15}$
$2\sigma =1-\frac{4}{15}$
$2\sigma =\frac{11}{15}$
$\sigma =\frac{11}{30}$
$\sigma \approx 0.3667$

Rounding off to two decimal places, we get:
$\sigma \approx 0.37$

Therefore, the value of Poisson's ratio for the material is 0.37.