Calculate the radius of the capillary tube if, when it is dipped vertially into a beaker of water, the water stands 35 cm higher in capillary tube than in the beaker. Surface of water is `0.073 Nm^(-1)`.

Explanation

To calculate the radius of the capillary tube, we can use the formula that relates the height of the liquid column in the capillary tube to the surface tension, density, and gravitational acceleration. The formula is given by:

\[ h = \frac{2 \sigma}{\rho g r} \]

Where:
- \( h \) = height of the liquid column (in meters)
- \( \sigma \) = surface tension of the liquid (in N/m)
- \( \rho \) = density of the liquid (in kg/m³)
- \( g \) = acceleration due to gravity (in m/s²)
- \( r \) = radius of the capillary tube (in meters)

### Step 1: Convert the height from cm to meters
Given that the height \( h \) is 35 cm, we convert it to meters:
\[ h = 35 \, \text{cm} = 0.35 \, \text{m} \]

### Step 2: Identify the known values
- Surface tension \( \sigma = 0.073 \, \text{N/m} \)
- Density of water \( \rho = 1000 \, \text{kg/m}^3 \)
- Acceleration due to gravity \( g = 9.8 \, \text{m/s}^2 \)

### Step 3: Rearrange the formula to solve for the radius \( r \)
Rearranging the formula to isolate \( r \):
\[ r = \frac{2 \sigma}{\rho g h} \]

### Step 4: Substitute the known values into the formula
Substituting the known values into the rearranged formula:
\[ r = \frac{2 \times 0.073}{1000 \times 9.8 \times 0.35} \]

### Step 5: Calculate the value of \( r \)
Calculating the numerator:
\[ 2 \times 0.073 = 0.146 \]

Calculating the denominator:
\[ 1000 \times 9.8 \times 0.35 = 3430 \]

Now, substituting these values into the equation for \( r \):
\[ r = \frac{0.146}{3430} \approx 4.26 \times 10^{-5} \, \text{m} \]

### Step 6: Final answer
Thus, the radius of the capillary tube is approximately:
\[ r \approx 4.3 \times 10^{-5} \, \text{m} \]