By sucking a straw a student can reduce the pressure in his lungs to `750 mm` of `Hg ("density")= 13.6 kg//cm^(3))` Using the straw, he can drink water from a glass up to a maximum depth of :

Options

A. 10.2 cm
B. 75.3 cm
C. 13.6 cm
D. 1.96 cm

Explanation

To solve the problem, we need to find the maximum depth of water that a student can drink using a straw when he reduces the pressure in his lungs to 750 mm of Hg.

### Step-by-Step Solution:

1. **Understand the Pressure Difference**:
When the student sucks on the straw, he creates a pressure difference between the atmospheric pressure and the pressure in his lungs. This pressure difference allows him to lift the water up the straw.

2. **Pressure Calculation**:
The pressure difference created by the reduction in lung pressure is given as:
\[ \Delta P = P_{\text{atm}} - P_{\text{lungs}} = P_{\text{atm}} - 750 \, \text{mm Hg} \]
For simplicity, we can consider atmospheric pressure \( P_{\text{atm}} \) to be 760 mm Hg.

3. **Calculate the Pressure Difference**:
The pressure difference can be calculated as:
\[ \Delta P = 760 \, \text{mm Hg} - 750 \, \text{mm Hg} = 10 \, \text{mm Hg} \]

4. **Relate Pressure Difference to Fluid Height**:
The pressure difference can also be expressed in terms of the height of the water column (h) that can be supported by this pressure difference:
\[ \Delta P = h \cdot \rho \cdot g \]
where \( \rho \) is the density of the fluid (water in this case) and \( g \) is the acceleration due to gravity.

5. **Convert Density of Mercury to Density of Water**:
The density of mercury is given as \( \rho_{\text{Hg}} = 13.6 \, \text{g/cm}^3 \) or \( 13600 \, \text{kg/m}^3 \). The density of water is \( \rho_{\text{water}} = 1000 \, \text{kg/m}^3 \).

6. **Calculate Maximum Height of Water (h)**:
Using the relationship between the pressure difference and the height of the water column:
\[ h = \frac{\Delta P \cdot \rho_{\text{Hg}}}{\rho_{\text{water}}} \]
Substituting the values:
\[ h = \frac{10 \, \text{mm Hg} \cdot 13.6 \, \text{g/cm}^3}{1 \, \text{g/cm}^3} \]
Since \( 1 \, \text{mm Hg} \) corresponds to a height of \( 1.36 \, \text{cm} \) of water, we can convert:
\[ h = 10 \cdot 13.6 = 136 \, \text{cm} \]

7. **Final Result**:
The maximum depth of water that the student can drink using the straw is:
\[ h = 136 \, \text{cm} \text{ or } 1.36 \, \text{m} \]