Question

Assertion: Bulk modulus of elasticity (K) represents the incompressibility of the material.
Reason: Bulk modulus of elasticity is proportional to change in pressure.
A. Both assertion and reason are correct and the reason is the correct explanation for the assertion.
B. Both assertion and reason are correct but the reason is not the correct explanation for the assertion.
C. The assertion is correct but the reason is incorrect.
D. Both assertion and reason are incorrect.

Answer 1

Hint: In order to answer this question it is good to know about a few things related to the bulk modulus. Bulk modulus is the ratio of volumetric stress to the volumetric strain of specific material, while the deformation of a material is within the elastic limit. In other words, the bulk modulus is just a numerical constant that describes the elastic properties of a material.

Complete step by step solution:
As we know that the bulk modulus is given by the ratio of pressure applied to the corresponding relative decrease in the volume of the material. Mathematically, it can be represented as,
$$K={\displaystyle \frac{dP}{\left({\displaystyle \frac{dV}{V}}\right)}}$$……….. (1)
$$\Rightarrow K={\displaystyle \frac{dP}{{\epsilon }_v}}$$
Here $${\displaystyle \frac{dV}{V}}={\epsilon }_v$$ and $${\epsilon }_v$$ is the volumetric strain.

We know that by the formula the bulk modulus is inversely proportional to compressibility i.e.,
$$\beta ={\displaystyle \frac{1}{k}}$$
Bulk modulus measures how good the body is to regain its original volume when it is being compressed. So, this represents the incompressibility of the material. By considering equation (1), we can say that the bulk modulus is directly proportional to the change in pressure.

Hence, option A is the correct answer.

Note: A body's volume will vary when it is subjected to a system of forces because of the stress the system places on the body. The bulk modulus gauges a body's resistance to outside pressures operating on it. Young's modulus measures the body's stiffness, whereas rigidity modulus or shear modulus measures resistance to shear failure.