The bulk modulus of a liquid is `3 xx 10^(10) Nm^(-2)`. The pressure required to reduce the volume of liquid by 2% is :

Options

A. `3 xx 10^8 Nm^(-2)`
B. `9 xx 10^8 Nm^(-2)`
C. `6 xx 10^8 Nm^(-2)`
D. `12 xx 10^8 Nm^(-2)`

Answer

To solve the problem, we need to find the pressure required to reduce the volume of a liquid by 2%. We will use the formula related to bulk modulus.

### Step-by-Step Solution:

1. **Understand the Bulk Modulus Formula**:
The bulk modulus \( B \) is defined as:
\[ B = -\frac{\Delta P}{\frac{\Delta V}{V}} \]
where:
- \( \Delta P \) is the change in pressure,
- \( \Delta V \) is the change in volume,
- \( V \) is the original volume.

2. **Rearranging the Formula**:
We need to isolate \( \Delta P \):
\[ \Delta P = -B \cdot \frac{\Delta V}{V} \]

3. **Substituting the Values**:
We know:
- The bulk modulus \( B = 3 \times 10^{10} \, \text{Nm}^{-2} \)
- The change in volume \( \Delta V \) is 2% of the original volume \( V \), which can be expressed as:
\[ \frac{\Delta V}{V} = -\frac{2}{100} = -0.02 \]

4. **Calculating \( \Delta P \)**:
Now substitute the values into the rearranged formula:
\[ \Delta P = -\left(3 \times 10^{10}\right) \cdot \left(-0.02\right) \]
Simplifying this gives:
\[ \Delta P = 3 \times 10^{10} \times 0.02 = 6 \times 10^{8} \, \text{Nm}^{-2} \]

5. **Final Answer**:
The pressure required to reduce the volume of the liquid by 2% is:
\[ \Delta P = 6 \times 10^{8} \, \text{Nm}^{-2} \]