Barometer is constructed using liquid . What would be height of liquid column when mercury barometer reads 76cm

Options

A. 1.36 m
B. 13.6 m
C. 136 m
D. 0.76 m

Answer

To find the height of the liquid column in a barometer constructed using a liquid with a density of 760 kg/m³ when the mercury barometer reads 76 cm, we can use the principle of hydrostatic pressure.

### Step-by-Step Solution:

1. **Understand the Concept**:
- A barometer measures atmospheric pressure. The height of the liquid column in the barometer is directly proportional to the atmospheric pressure and inversely proportional to the density of the liquid used in the barometer.

2. **Identify Given Values**:
- Height of mercury column (h₁) = 76 cm = 0.76 m (convert to meters for consistency).
- Density of mercury (ρ₁) = 13600 kg/m³.
- Density of the liquid in the second barometer (ρ₂) = 760 kg/m³.

3. **Use the Hydrostatic Pressure Equation**:
- The pressure exerted by the mercury column (P₁) is equal to the pressure exerted by the liquid column (P₂).
- The pressure due to a column of liquid is given by the formula:
\[ P = \rho g h \]
- Therefore, for mercury:
\[ P₁ = \rho₁ g h₁ \]
- And for the liquid:
\[ P₂ = \rho₂ g h₂ \]
- Since P₁ = P₂, we can set the equations equal:
\[ \rho₁ g h₁ = \rho₂ g h₂ \]

4. **Cancel out g**:
- The acceleration due to gravity (g) is common in both sides and can be canceled out:
\[ \rho₁ h₁ = \rho₂ h₂ \]

5. **Rearrange to Find h₂**:
- Rearranging the equation gives:
\[ h₂ = \frac{\rho₁ h₁}{\rho₂} \]

6. **Substitute the Known Values**:
- Substitute the known values into the equation:
\[ h₂ = \frac{13600 \, \text{kg/m}^3 \times 0.76 \, \text{m}}{760 \, \text{kg/m}^3} \]

7. **Calculate h₂**:
- Performing the calculation:
\[ h₂ = \frac{10336 \, \text{kg/m}^2}{760 \, \text{kg/m}^3} \]
\[ h₂ = 13.6 \, \text{m} \]

### Final Answer:
The height of the liquid column when the mercury barometer reads 76 cm is **13.6 meters**.