If the surface tension of water is 0.06 N/m, then the capillary rise in a tube of diameter 1mm is `(theta=0^(@)`)

Options

A. 1.22 cm
B. 2.44 cm
C. 3.12 cm
D. 3.86 cm

Explanation

To solve the problem of finding the capillary rise in a tube of diameter 1 mm with a surface tension of water of 0.06 N/m, we can follow these steps:

### Step 1: Identify the given values
- Surface tension (T) = 0.06 N/m
- Diameter of the tube (d) = 1 mm = 1 x 10^-3 m
- Radius of the tube (R) = d/2 = (1 x 10^-3 m) / 2 = 0.5 x 10^-3 m = 0.0005 m
- Angle (θ) = 0° (cos 0° = 1)
- Density of water (ρ) = 1000 kg/m³ (or 10^3 kg/m³)
- Acceleration due to gravity (g) = 10 m/s² (approximately)

### Step 2: Use the formula for capillary rise
The formula for the height of capillary rise (h) is given by:

\[ h = \frac{2T \cos \theta}{\rho R g} \]

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:

\[ h = \frac{2 \times 0.06 \, \text{N/m} \times \cos(0°)}{1000 \, \text{kg/m}^3 \times 0.0005 \, \text{m} \times 10 \, \text{m/s}^2} \]

Since \(\cos(0°) = 1\), we can simplify this to:

\[ h = \frac{2 \times 0.06}{1000 \times 0.0005 \times 10} \]

### Step 4: Calculate the denominator
Calculating the denominator:

\[ 1000 \times 0.0005 \times 10 = 5 \]

### Step 5: Calculate the height (h)
Now substituting back into the equation for h:

\[ h = \frac{2 \times 0.06}{5} \]

Calculating this gives:

\[ h = \frac{0.12}{5} = 0.024 \, \text{m} \]

### Step 6: Convert to centimeters
To convert meters to centimeters:

\[ h = 0.024 \, \text{m} \times 100 \, \text{cm/m} = 2.4 \, \text{cm} \]

### Final Result
Thus, the capillary rise in the tube is **2.4 cm**.

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