Question

A material has a youngs modulus of 1.25 105 n/mm2 and a poissons ratio of 0.25. The bulk modulus of the material will be

Answer 1

Given:

A material has a youngs modulus of 1.25×10⁵ N/m² and a poissons ratio of 0.25.

To find:

Value of Bulk Modulus.

Calculation:

This type of questions always appear in competitive exams and hence kindly remember the following equation relating the Young's Modulus, Poisson's ratio and Bulk Modulus.

$\boxed{ \bold{K = \dfrac{ \gamma }{3(1 - 2 \sigma)} }}$

Here "K" is Bulk Modulus , $\gamma$ is Young's Modulus , $\sigma$ is Poisson's ratio.

Putting the available values:

$\sf{ = > K = \dfrac{ 1.25 \times {10}^{ - 5} }{3 \bigg \{1 - 2 (0.25) \bigg \}} }$

$\sf{ = > K = \dfrac{ 1.25 \times {10}^{ - 5} }{3 \bigg \{1 - 0.5 \bigg \}} }$

$\sf{ = > K = \dfrac{ 1.25 \times {10}^{ - 5} }{3 \bigg \{0.5 \bigg \}} }$

$\sf{ = > K = \dfrac{ 1.25 \times 2 \times {10}^{ - 5} }{3 } }$

$\sf{ = > K = \dfrac{ 2.5 \times {10}^{ - 5} }{3 } }$

$\sf{ = > K = 0.83 \times {10}^{ - 5} \:Pa }$

So, Bulk Modulus is 0.83 × 10^(-5) Pascal.