Question:
The ratio of hydrostatic stress to volumetric strain is known as ______.
The ratio of hydrostatic stress to volumetric strain is known as ______.
Show Hint
Compare the ratio given in the question with the standard definitions of Young's modulus, bulk modulus, compressibility, and Poisson's ratio.
Updated On: Aug 5, 2026
- Bulk modulus
- Compressibility
- Poisson's ratio
- Young's modulus
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Understanding the Question:
The question tests a basic definition from the theory of elasticity.
We are asked which elastic constant is obtained when hydrostatic (volumetric) stress is divided by volumetric strain.
This constant tells us how much a material resists a change in its volume when it is squeezed equally from every direction.
Step 2: Key Formula or Approach:
When a body is subjected to equal stress from every direction (hydrostatic stress \( \sigma_v \)), it undergoes a change in volume \( \Delta V \) from its original volume \( V_0 \).
The volumetric strain is defined as \( \epsilon_v = \Delta V / V_0 \).
The elastic constant that connects the two is called the bulk modulus.
\[ K = \frac{\sigma_v}{\epsilon_v} = \frac{\text{hydrostatic stress}}{\text{volumetric strain}} \]
Step 3: Detailed Explanation:
Option (A) Bulk modulus: by definition this is exactly the ratio of hydrostatic stress to volumetric strain, so this matches the question directly.
Option (B) Compressibility: this is defined as the reciprocal of bulk modulus, \( 1/K \), which connects strain to stress, not stress to strain, so it is the wrong pairing.
Option (C) Poisson's ratio: this compares lateral strain to longitudinal strain under a uniaxial load, it has nothing to do with hydrostatic loading.
Option (D) Young's modulus: this is the ratio of longitudinal stress to longitudinal strain under a simple axial pull, not a volumetric loading condition.
Final Answer:
The ratio of hydrostatic stress to volumetric strain is called the bulk modulus.
\[ \boxed{\text{Bulk modulus}} \]
The question tests a basic definition from the theory of elasticity.
We are asked which elastic constant is obtained when hydrostatic (volumetric) stress is divided by volumetric strain.
This constant tells us how much a material resists a change in its volume when it is squeezed equally from every direction.
Step 2: Key Formula or Approach:
When a body is subjected to equal stress from every direction (hydrostatic stress \( \sigma_v \)), it undergoes a change in volume \( \Delta V \) from its original volume \( V_0 \).
The volumetric strain is defined as \( \epsilon_v = \Delta V / V_0 \).
The elastic constant that connects the two is called the bulk modulus.
\[ K = \frac{\sigma_v}{\epsilon_v} = \frac{\text{hydrostatic stress}}{\text{volumetric strain}} \]
Step 3: Detailed Explanation:
Option (A) Bulk modulus: by definition this is exactly the ratio of hydrostatic stress to volumetric strain, so this matches the question directly.
Option (B) Compressibility: this is defined as the reciprocal of bulk modulus, \( 1/K \), which connects strain to stress, not stress to strain, so it is the wrong pairing.
Option (C) Poisson's ratio: this compares lateral strain to longitudinal strain under a uniaxial load, it has nothing to do with hydrostatic loading.
Option (D) Young's modulus: this is the ratio of longitudinal stress to longitudinal strain under a simple axial pull, not a volumetric loading condition.
Final Answer:
The ratio of hydrostatic stress to volumetric strain is called the bulk modulus.
\[ \boxed{\text{Bulk modulus}} \]
Was this answer helpful?
0
0
Top GATE PI Strength of Materials Questions
- For a mild steel specimen subjected to uniaxial tensile load, which of the following is/are TRUE?
- In the truss shown in the figure, member AC is an inextensible string, other members are rigid, and ABCD is a square with each side of length a. The maximum value of force F (in kN) for which the truss will remain in static equilibrium is _____ . (Rounded off to 2 decimal places)
- In a forming operation, the plastic deformation of a steel specimen starts under plane stress condition, where the principal stresses are \(σ_1=200\ Mpa\) and \(σ_2 = 100\ Mpa\). If the steel specimen follows von-Mises yield criterion, then the uniaxial tensile yield strength (in Mpa) of this steel material is ____ . (Rounded off to 1 decimal place)
Consider the truss shown in the figure. The members AB, BC, and CA are all rigid and form an equilateral triangle. The contact between roller and ground at C is frictionless. If the self-weight of members is neglected, the force in member BC in N is (negative sign should be used if the force is compressive and positive if the force in the member is tensile) _________.
Top GATE PI Questions
- In an air-standard Otto cycle, the pressure and temperature of air just before the compression stroke are 200 kPa and 26.85 °C, respectively. The combustion process is assumed to be a constant volume process, where 1.02 MJ/kg heat is added. The cycle efficiency is 50%. The adiabatic index \(γ\) and specific heat at constant volume \(C_v\) can be considered to be constant during the process (corresponding values taken at the mean cycle temperature).
Assuming that the ideal gas law is applicable, \(γ = \frac 43\) and \(c_v= 0.85\ kJ/kg-K\), the maximum pressure (in MPa) reached during the cycle is _____ . (Rounded off to 1 decimal place) - A metallic cylindrical pressure vessel, used to store compressed air in a plant, has 1 m mean radius and 4 mm wall thickness. The maximum allowable normal and shear stresses in the cylindrical portion of the vessel are 100 MPa and 40 MPa, respectively. Considering only these data in the design, the maximum allowable internal gauge pressure (in MPa) of the compressed air is ______ . (Rounded off to 2 decimal places)
- A flat belt drive with pulley of r = 20 cm radius is designed to transmit 6.283 kW power at 600 RPM. In the figure, τ is the corresponding torque. If the coefficient of static friction between the belt and the pulley is 0.3, then the minimum value of the tightening force F (in kN) required to prevent the belt slip is _____ . (Rounded off 2 decimal places)
- Mild steel plates are welded to make butt joints by arc welding with 85% heat transfer efficiency ignoring other losses. The first weld joint is made by selecting arc voltage of 30 V and current of 180 A with a welding speed of 6 mm/s. Using identical plates, a second weld joint is made with the same arc voltage and a welding speed of 8 mm/s. If both the welds have the same heat input, then the welding current (in A) for the second weld joint is _____. (Answer in integer)
- In a single pass cold rolling operation, a flat plate is reduced to a thickness of 3 mm. In this operation, two rolls of diameter 400 mm each are rotating in opposite direction at 300 RPM, and the elastic deflection of these rolls is negligible. The angle of bite is 10°. If the neutral point is present at an angle of 7° from the exit side, then the thickness of the plate (in mm) at the neutral point is _____ . (Rounded off to 1 decimal place)
View More Questions