A metal block is experiencing an atmospheric pressure of `1 xx 10^(5)N//m^(2)`, when the same block is placed vacuum chamber, the freactional change in its volume is (the bulk modulus of metal is `1.25 xx 10^(11) N//m^(2)`)

Options

A. `4 xx 10^(-7)`
B. `2 xx 10^(-7)`
C. `8 xx 10^(-7)`
D. `1 xx 10^(-7)`

Explanation

To solve the problem of finding the fractional change in volume of a metal block when it is placed in a vacuum chamber, we can follow these steps:

### Step 1: Understand the Problem
The metal block is initially under atmospheric pressure, which is given as \( P_1 = 1 \times 10^5 \, \text{N/m}^2 \). When placed in a vacuum chamber, the pressure becomes \( P_2 = 0 \, \text{N/m}^2 \). We need to find the fractional change in volume \( \frac{\Delta V}{V} \).

### Step 2: Calculate the Change in Pressure
The change in pressure \( \Delta P \) can be calculated as:
\[ \Delta P = P_1 - P_2 = 1 \times 10^5 \, \text{N/m}^2 - 0 \, \text{N/m}^2 = 1 \times 10^5 \, \text{N/m}^2 \]

### Step 3: Use the Bulk Modulus Formula
The relationship between the change in volume and the bulk modulus \( B \) is given by:
\[ \frac{\Delta V}{V} = -\frac{\Delta P}{B} \]
Here, \( B \) is the bulk modulus of the metal, which is given as \( B = 1.25 \times 10^{11} \, \text{N/m}^2 \).

### Step 4: Substitute the Values into the Formula
Now, substituting the values of \( \Delta P \) and \( B \) into the formula:
\[ \frac{\Delta V}{V} = -\frac{1 \times 10^5 \, \text{N/m}^2}{1.25 \times 10^{11} \, \text{N/m}^2} \]

### Step 5: Calculate the Fractional Change in Volume
Calculating the right-hand side:
\[ \frac{\Delta V}{V} = -\frac{1 \times 10^5}{1.25 \times 10^{11}} = -\frac{1}{1.25} \times 10^{-6} = -0.8 \times 10^{-6} \]
This simplifies to:
\[ \frac{\Delta V}{V} = -8 \times 10^{-7} \]

### Conclusion
The fractional change in volume of the metal block when placed in the vacuum chamber is:
\[ \frac{\Delta V}{V} = -8 \times 10^{-7} \]

---