The height of mercury which exerts the same pressure as 20 cm of water column, is

Options

A. 1.47 cm
B. 14.8cm
C. 148 cm
D. None of these

Answer

To find the height of mercury that exerts the same pressure as a 20 cm column of water, we will use the formula for pressure:

\[ P = \rho \cdot g \cdot h \]

where:
- \( P \) = pressure
- \( \rho \) = density of the fluid
- \( g \) = acceleration due to gravity
- \( h \) = height of the fluid column

### Step 1: Calculate the pressure exerted by the water column
Given:
- Height of water column, \( h_w = 20 \, \text{cm} = 0.2 \, \text{m} \)
- Density of water, \( \rho_w = 1000 \, \text{kg/m}^3 \) (or \( 1 \, \text{g/cm}^3 \))

Using the formula for pressure:
\[ P_w = \rho_w \cdot g \cdot h_w \]
\[ P_w = 1000 \cdot 9.8 \cdot 0.2 \]
\[ P_w = 1960 \, \text{Pa} \]

### Step 2: Set up the equation for the pressure exerted by the mercury column
Let \( h_m \) be the height of the mercury column. The density of mercury is:
- \( \rho_m = 13600 \, \text{kg/m}^3 \) (or \( 13.6 \, \text{g/cm}^3 \))

The pressure exerted by the mercury column is:
\[ P_m = \rho_m \cdot g \cdot h_m \]

### Step 3: Equate the pressures
Since both pressures are equal:
\[ P_w = P_m \]
\[ 1000 \cdot 9.8 \cdot 0.2 = 13600 \cdot 9.8 \cdot h_m \]

### Step 4: Simplify the equation
We can cancel \( 9.8 \) from both sides:
\[ 1000 \cdot 0.2 = 13600 \cdot h_m \]
\[ 200 = 13600 \cdot h_m \]

### Step 5: Solve for \( h_m \)
\[ h_m = \frac{200}{13600} \]
\[ h_m = \frac{1}{68} \]
\[ h_m \approx 0.0147 \, \text{m} = 1.47 \, \text{cm} \]

### Final Answer
The height of mercury that exerts the same pressure as a 20 cm water column is approximately **1.47 cm**.

---