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 solve the problem of finding the fractional change in volume of a glass slab subjected to a pressure of 10 atm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Data:**
- Pressure (P) = 10 atm
- Bulk modulus of glass (B) = 37 x 10^9 N/m²
- Conversion factor: 1 atm = 1 x 10^5 N/m²

2. **Convert Pressure from atm to N/m²:**
- Since 1 atm = 1 x 10^5 N/m²,
- Therefore, 10 atm = 10 x (1 x 10^5 N/m²) = 10 x 10^5 N/m² = 1 x 10^6 N/m².

3. **Use the Formula for Fractional Change in Volume:**
- The fractional change in volume (ΔV/V) can be calculated using the formula:
\[ \frac{\Delta V}{V} = \frac{P}{B} \]
- Where P is the pressure applied, and B is the bulk modulus.

4. **Substitute the Values into the Formula:**
- Substitute P = 1 x 10^6 N/m² and B = 37 x 10^9 N/m² into the formula:
\[ \frac{\Delta V}{V} = \frac{1 \times 10^6}{37 \times 10^9} \]

5. **Calculate the Fractional Change in Volume:**
- Performing the calculation:
\[ \frac{\Delta V}{V} = \frac{1}{37} \times \frac{10^6}{10^9} = \frac{1}{37} \times 10^{-3} \]
- This simplifies to:
\[ \frac{\Delta V}{V} = \frac{10^{-3}}{37} \approx 2.7 \times 10^{-5} \]

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

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