If stress-strain relation for volametric change is in the from `(DeltaV)/(V_(0))= KP` where P is applied uniform pressure, then K stands for

Options

A. shear modulus
B. compressibility
C. Young's modulus
D. bulk modulus

Explanation

To solve the question regarding the stress-strain relation for volumetric change given by the equation \(\frac{\Delta V}{V_0} = K P\), we need to identify what the constant \(K\) represents among the options provided: shear modulus, compressibility, Young's modulus, and bulk modulus.

### Step-by-Step Solution:

1. **Understanding the Equation**:
The equation \(\frac{\Delta V}{V_0} = K P\) describes the relationship between the change in volume (\(\Delta V\)), the original volume (\(V_0\)), and the applied uniform pressure (\(P\)). Here, \(K\) is a proportionality constant.

2. **Identifying the Options**:
- **Shear Modulus**: This is defined as the ratio of shear stress to shear strain. It is not applicable here since the equation involves volumetric change, not shear.
- **Young's Modulus**: This is defined as the ratio of tensile stress to tensile strain. Again, this is not relevant to volumetric changes.
- **Bulk Modulus**: This is defined as the measure of a substance's resistance to uniform compression. It relates to volumetric strain and is defined as \(B = -\frac{P}{\frac{\Delta V}{V_0}}\).
- **Compressibility**: This is defined as the reciprocal of bulk modulus, given by \(\beta = \frac{1}{B}\). It is also related to how much a material compresses under pressure.

3. **Relating \(K\) to Bulk Modulus**:
From the definition of bulk modulus, we can rearrange it to find a relationship with compressibility:
\[ B = -\frac{P}{\frac{\Delta V}{V_0}} \implies \frac{\Delta V}{V_0} = -\frac{P}{B} \]
If we compare this with our original equation \(\frac{\Delta V}{V_0} = K P\), we can see that \(K\) must be related to compressibility.

4. **Conclusion**:
Since \(K\) is proportional to the change in volume per unit pressure, and recognizing that compressibility is defined as the change in volume per unit pressure, we conclude that \(K\) represents compressibility.

### Final Answer:
Thus, \(K\) stands for **compressibility**.

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