Vessel of `1xx10^(-3) m^(3)` volume contains an oil. If a pressure of `1.2xx10^(5) N//m^(2)` is applied on it , then volume decreases by `0.3xx10(-3) m^(3)`. The bulk modulus of oil is

Options

A. (a) `6xx10^(10) N//m^(2)`
B. (b) `4xx10^(5) N//m^(2)`
C. (c) `2xx10^(7) N//m^(2)`
D. (d) `1xx10^(6) N//m^(2) `

Explanation

To find the bulk modulus of the oil, we can use the formula for bulk modulus (K):

\[ K = -\frac{\Delta P}{\frac{\Delta V}{V}} \]

Where:
- \( \Delta P \) is the change in pressure,
- \( \Delta V \) is the change in volume,
- \( V \) is the original volume.

### Step 1: Identify the given values
- Original volume, \( V = 1 \times 10^{-3} \, m^3 \)
- Change in volume, \( \Delta V = 0.3 \times 10^{-3} \, m^3 \)
- Applied pressure, \( P = 1.2 \times 10^{5} \, N/m^2 \)

### Step 2: Calculate the change in pressure
Since the pressure is applied, we can consider the change in pressure as:

\[ \Delta P = P = 1.2 \times 10^{5} \, N/m^2 \]

### Step 3: Calculate the ratio \( \frac{\Delta V}{V} \)
Now, we need to calculate the ratio of the change in volume to the original volume:

\[ \frac{\Delta V}{V} = \frac{0.3 \times 10^{-3}}{1 \times 10^{-3}} = 0.3 \]

### Step 4: Substitute values into the bulk modulus formula
Now, substitute the values into the bulk modulus formula:

\[ K = -\frac{1.2 \times 10^{5}}{0.3} \]

### Step 5: Calculate the bulk modulus
Now, calculate the value:

\[ K = -\frac{1.2 \times 10^{5}}{0.3} = -4 \times 10^{5} \, N/m^2 \]

Since bulk modulus is a positive quantity, we take the absolute value:

\[ K = 4 \times 10^{5} \, N/m^2 \]

### Final Answer
The bulk modulus of the oil is \( 4 \times 10^{5} \, N/m^2 \).

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