Question

The ratio of hydraulic stress to the corresponding strain is known as-
A. Compressibility.
B. Bulk modulus.
C. Young’s modulus.
D. Rigidity modulus.
E. Expansion coefficient.

Answer 1

Hint: Firstly we must have a basic idea of hydraulic stress and strain. Basics of bulk modulus of elasticity will also be used in this question. Use the understanding of their mathematical expressions to answer the question correctly.

Complete answer:
We will firstly discuss what hydraulic stress and its corresponding stress means.
Hydraulic stress:
Hydraulic stress is defined as the restoring force acting per unit area when force is applied by a fluid on any object or body in contact with the fluid.

Strain :
The strain is simply the measure of how much an object is stretched or deformed.
Now we will go on the question part
The bulk modulus of elasticity is defined as the ratio of hydraulic stress to the corresponding volumetric strain within the elastic limit.
Now, we will see the equation or the relation between hydraulic stress and its corresponding strain.
\[\begin{align}
  & K=\dfrac{FV}{A\Delta V}=\dfrac{\Delta p.V}{\Delta V} \\
 & Where,\Delta p=\dfrac{F}{A} \\
\end{align}\]
\[\Delta p\]=change in pressure
So from the above solution, we can say that the ratio of hydraulic stress and its corresponding stress is known as the bulk modulus.

Note: Hooke’s law states that if the deformation is small, the stress in a body is directly proportional to the corresponding strain. The ratio of stress over strain corresponds to Young’s, Bulk, or shear modulus depending upon the system under consideration. Within the elastic limit, the ratio of normal stress to the volumetric strain is known as the bulk modulus of elasticity. The compressibility of a body is also defined as the reciprocal of the bulk modulus.