A woman is enjoying a cold drink while lying on a beach. The acceleration due to gravity at her location is 9.85 m/`s^(8)`. What gauge pressure must exist in the woman's mouth if she is drinking through a straw extending 0.085 m above the surface of the drink? (Assume the drink has a density of 1015 kg/`m^(3)`.)

Options

A. 850 Pa
B. 970 Pa
C. 1100 Pa
D. 2100 Pa

Answer

To find the gauge pressure that must exist in the woman's mouth while drinking through a straw, we can use the hydrostatic pressure formula, which relates the pressure difference to the height of the liquid column.

### Step-by-Step Solution:

1. **Identify the given values:**
- Density of the drink, \( \rho = 1015 \, \text{kg/m}^3 \)
- Acceleration due to gravity, \( g = 9.85 \, \text{m/s}^2 \)
- Height of the straw above the surface of the drink, \( h = 0.085 \, \text{m} \)

2. **Use the hydrostatic pressure formula:**
The gauge pressure \( P \) at the height of the straw can be calculated using the formula:
\[ P = \rho g h \]

3. **Substitute the known values into the formula:**
\[ P = 1015 \, \text{kg/m}^3 \times 9.85 \, \text{m/s}^2 \times 0.085 \, \text{m} \]

4. **Calculate the pressure:**
- First, calculate \( \rho g \):
\[ \rho g = 1015 \times 9.85 = 10000.75 \, \text{N/m}^3 \]
- Now multiply by \( h \):
\[ P = 10000.75 \, \text{N/m}^3 \times 0.085 \, \text{m} = 850.06 \, \text{Pa} \]

5. **Round to appropriate significant figures:**
The gauge pressure is approximately:
\[ P \approx 850 \, \text{Pa} \]

### Final Answer:
The gauge pressure that must exist in the woman's mouth is approximately **850 Pascal**.

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