If the atmospheric pressure is 76 cm of Hg at what depth of water the pressure will becomes 2 atmospheres nearly.

Options

A. 862 cm
B. 932 cm
C. 982 cm
D. 1033 cm

Explanation

To solve the problem of finding the depth of water at which the pressure becomes 2 atmospheres, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Data:**
- Atmospheric pressure (P₀) = 76 cm of Hg
- We need to find the depth of water (h) where the pressure becomes 2 atmospheres.

2. **Convert Atmospheric Pressure to a Common Unit:**
- Since 1 atmosphere is equivalent to 76 cm of Hg, 2 atmospheres will be:
\[ P = 2 \times P₀ = 2 \times 76 \text{ cm Hg} = 152 \text{ cm Hg} \]

3. **Calculate the Pressure Difference:**
- The pressure due to the water column at depth h must equal the difference between the total pressure (2 atmospheres) and the atmospheric pressure:
\[ P_{\text{water}} = P - P₀ = 152 \text{ cm Hg} - 76 \text{ cm Hg} = 76 \text{ cm Hg} \]

4. **Use the Hydrostatic Pressure Formula:**
- The pressure due to a column of liquid is given by:
\[ P = h \cdot \rho \cdot g \]
- Here, we can equate the pressure due to the water column to the pressure difference we calculated:
\[ h \cdot \rho_{\text{water}} \cdot g = 76 \text{ cm Hg} \]

5. **Convert the Pressure of Mercury to Water:**
- The density of mercury (ρₕ) is approximately 13.6 g/cm³, and the density of water (ρₜ) is approximately 1 g/cm³. Therefore, we can relate the heights of the mercury and water columns:
\[ h_{\text{water}} \cdot \rho_{\text{water}} \cdot g = h_{\text{Hg}} \cdot \rho_{\text{Hg}} \cdot g \]
- This simplifies to:
\[ h_{\text{water}} = h_{\text{Hg}} \cdot \frac{\rho_{\text{Hg}}}{\rho_{\text{water}}} \]
- Substituting the values:
\[ h_{\text{water}} = 76 \text{ cm} \cdot \frac{13.6}{1} = 76 \cdot 13.6 = 1033.6 \text{ cm} \]

6. **Conclusion:**
- The depth of water at which the pressure becomes nearly 2 atmospheres is approximately **1033.6 cm**.

### Final Answer:
The depth of water required for the pressure to become 2 atmospheres is **1033.6 cm**.

---