Question:easy
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
The Correct Option is A
Solution and Explanation
Step 1: Setting Up the Elastic Constants:
In solid mechanics there are four common elastic constants: Young's modulus $E$, shear modulus $G$, bulk modulus $K$, and Poisson's ratio $\nu$.
Each one is defined as a ratio of a particular type of stress to the matching type of strain, so the fastest way to answer this question is to line up all four definitions side by side.
Step 2: Comparing the Definitions:
$E$ = longitudinal stress divided by longitudinal strain, this applies to simple tension or compression.
$G$ = shear stress divided by shear strain, this applies to twisting or sliding action.
$K$ = hydrostatic (volumetric) stress divided by volumetric strain, this applies to uniform squeezing from all sides.
$\nu$ = lateral strain divided by longitudinal strain, notice this is a ratio of two strains, not stress to strain at all.
Step 3: Matching to the Question:
The question specifically asks for hydrostatic stress divided by volumetric strain, and from the list above this description belongs only to the bulk modulus $K$.
Compressibility looks similar but is actually $1/K$, that is strain divided by stress, so it is the inverse quantity and not the one described here.
Final Answer:
Matching the ratio in the question to the standard elastic constant definitions gives the bulk modulus.
\[ \boxed{K = \dfrac{\text{hydrostatic stress}}{\text{volumetric strain}} \Rightarrow \text{Bulk modulus}} \]
In solid mechanics there are four common elastic constants: Young's modulus $E$, shear modulus $G$, bulk modulus $K$, and Poisson's ratio $\nu$.
Each one is defined as a ratio of a particular type of stress to the matching type of strain, so the fastest way to answer this question is to line up all four definitions side by side.
Step 2: Comparing the Definitions:
$E$ = longitudinal stress divided by longitudinal strain, this applies to simple tension or compression.
$G$ = shear stress divided by shear strain, this applies to twisting or sliding action.
$K$ = hydrostatic (volumetric) stress divided by volumetric strain, this applies to uniform squeezing from all sides.
$\nu$ = lateral strain divided by longitudinal strain, notice this is a ratio of two strains, not stress to strain at all.
Step 3: Matching to the Question:
The question specifically asks for hydrostatic stress divided by volumetric strain, and from the list above this description belongs only to the bulk modulus $K$.
Compressibility looks similar but is actually $1/K$, that is strain divided by stress, so it is the inverse quantity and not the one described here.
Final Answer:
Matching the ratio in the question to the standard elastic constant definitions gives the bulk modulus.
\[ \boxed{K = \dfrac{\text{hydrostatic stress}}{\text{volumetric strain}} \Rightarrow \text{Bulk modulus}} \]
Was this answer helpful?
0
