A glass slab is subjected to a pressure of 10 atm. The fractional change in its volume is
(Bulk modalus of glass `=37 xx 10^(9) Nm^(-2), 1 atm= 1 xx 10^(5) N m^(-2)`)

Options

A. `2.7 xx10^(-2)`
B. `2.7 xx 10^(-3)`
C. `2.7 xx 10^(-4)`
D. `2.7 xx 10^(-5)`

Explanation

To find the fractional change in volume of a glass slab subjected to a pressure of 10 atm, we can use the formula related to bulk modulus. The bulk modulus (K) is defined as:

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

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

From this equation, we can rearrange it to find the fractional change in volume:

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

### Step-by-step Solution:

1. **Convert Pressure from atm to N/m²**:
Given that \( 1 \text{ atm} = 1 \times 10^5 \text{ N/m}^2 \), we first convert the pressure from atm to N/m².
\[ P = 10 \text{ atm} = 10 \times 1 \times 10^5 \text{ N/m}^2 = 10^6 \text{ N/m}^2 \]

2. **Substitute the Values into the Formula**:
We know the bulk modulus of glass \( K = 37 \times 10^9 \text{ N/m}^2 \). Now, we can substitute the values of \( P \) and \( K \) into the rearranged formula:
\[ \frac{\Delta V}{V} = -\frac{10^6}{37 \times 10^9} \]

3. **Calculate the Fractional Change in Volume**:
Now we perform the division:
\[ \frac{\Delta V}{V} = -\frac{10^6}{37 \times 10^9} = -\frac{1}{37 \times 10^3} \]
Simplifying further:
\[ \frac{\Delta V}{V} = -\frac{1}{37000} \approx -2.7 \times 10^{-5} \]

4. **Interpret the Result**:
The negative sign indicates a decrease in volume due to the applied pressure. Therefore, the fractional change in volume is approximately:
\[ \frac{\Delta V}{V} \approx -2.7 \times 10^{-5} \]

### Final Answer:
The fractional change in volume of the glass slab is approximately \( -2.7 \times 10^{-5} \).