The bulk modulus for an incompresssible liquid is

Options

A. zero
B. unity
C. infinity
D. between 0 and 1

Explanation

To find the bulk modulus for an incompressible liquid, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Bulk Modulus**:
The bulk modulus (K) is defined as the measure of a substance's resistance to uniform compression. It is mathematically given by the formula:
\[ K = -\frac{\Delta P}{\Delta V/V} \]
where \(\Delta P\) is the change in pressure, \(\Delta V\) is the change in volume, and \(V\) is the original volume.

2. **Consider the Properties of an Incompressible Liquid**:
An incompressible liquid is one that does not change its volume under pressure. Therefore, the change in volume (\(\Delta V\)) for an incompressible liquid is zero.

3. **Substitute \(\Delta V = 0\) into the Bulk Modulus Formula**:
Since \(\Delta V = 0\), we can substitute this into the bulk modulus formula:
\[ K = -\frac{\Delta P}{0/V} \]
This simplifies to:
\[ K = -\frac{\Delta P}{0} \]

4. **Analyze the Result**:
Dividing by zero is undefined in mathematics, but in the context of bulk modulus, it indicates that the liquid cannot be compressed at all. Therefore, we can say:
\[ K = \infty \]
This means that the bulk modulus of an incompressible liquid is effectively infinite.

5. **Conclusion**:
Thus, the bulk modulus for an incompressible liquid is:
\[ K = \infty \]