When a body having a volume of `10^(-3) m^(3)` is pressed by a pressure of `4 xx 10^(4) N //m^(2)`, its volume decreases by `0.2 xx 10^(-6) m^(3)`. Calculate the bulk modulus of the body.

Explanation

To calculate the bulk modulus of the body, we can follow these steps:

### Step 1: Write down the formula for bulk modulus
The bulk modulus (K) can be calculated using the formula:
\[ K = -\frac{P}{\frac{\Delta V}{V}} \]
where:
- \( P \) is the pressure applied,
- \( \Delta V \) is the change in volume,
- \( V \) is the original volume.

### Step 2: Identify the given values
From the problem, we have:
- Original volume, \( V = 10^{-3} \, m^3 \)
- Pressure, \( P = 4 \times 10^{4} \, N/m^2 \)
- Change in volume, \( \Delta V = -0.2 \times 10^{-6} \, m^3 \) (Note: It is negative because it is a decrease)

### Step 3: Substitute the values into the formula
Substituting the values into the bulk modulus formula:
\[ K = -\frac{4 \times 10^{4}}{\frac{-0.2 \times 10^{-6}}{10^{-3}}} \]

### Step 4: Simplify the denominator
Calculate the change in volume per unit volume:
\[ \frac{\Delta V}{V} = \frac{-0.2 \times 10^{-6}}{10^{-3}} = -0.2 \times 10^{-3} = -2 \times 10^{-4} \]

### Step 5: Substitute back into the formula
Now, substitute this value back into the equation for bulk modulus:
\[ K = -\frac{4 \times 10^{4}}{-2 \times 10^{-4}} \]

### Step 6: Calculate the bulk modulus
Now, calculate \( K \):
\[ K = \frac{4 \times 10^{4}}{2 \times 10^{-4}} = 2 \times 10^{8} \, N/m^2 \]

### Final Answer
Thus, the bulk modulus of the body is:
\[ K = 2 \times 10^{8} \, N/m^2 \]

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