Calculate the rise of water inside a clean glass capillary tube of radius 0.1 mm, when immersed in water of surface tension `7xx10^(-2)N//m.` The angle of contact between water and glass is zero, density of water is 1000 kg/`m^(3),g=9.8m//s^(2)`

Answer

To calculate the rise of water inside a clean glass capillary tube, we can use the formula for capillary rise:

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

Where:
- \( h \) = height of the liquid column (rise of water)
- \( T \) = surface tension of the liquid (water in this case)
- \( \theta \) = angle of contact (given as 0 degrees)
- \( r \) = radius of the capillary tube
- \( \rho \) = density of the liquid (water)
- \( g \) = acceleration due to gravity

### Step 1: Convert the radius from mm to meters
The radius of the capillary tube is given as 0.1 mm. To convert this to meters:

\[ r = 0.1 \, \text{mm} = 0.1 \times 10^{-3} \, \text{m} = 1 \times 10^{-4} \, \text{m} \]

### Step 2: Identify the values
- Surface tension \( T = 7 \times 10^{-2} \, \text{N/m} \)
- Angle of contact \( \theta = 0^\circ \) (thus \( \cos \theta = 1 \))
- Density of water \( \rho = 1000 \, \text{kg/m}^3 \)
- Acceleration due to gravity \( g = 9.8 \, \text{m/s}^2 \)

### Step 3: Substitute the values into the formula
Now we can substitute the values into the capillary rise formula:

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

Substituting the known values:

\[ h = \frac{2 \times (7 \times 10^{-2}) \times 1}{(1 \times 10^{-4}) \times (1000) \times (9.8)} \]

### Step 4: Calculate the numerator
Calculate the numerator:

\[ 2 \times (7 \times 10^{-2}) \times 1 = 0.14 \, \text{N/m} \]

### Step 5: Calculate the denominator
Calculate the denominator:

\[ (1 \times 10^{-4}) \times (1000) \times (9.8) = 0.098 \, \text{N} \]

### Step 6: Calculate the height \( h \)
Now, substitute the numerator and denominator back into the equation:

\[ h = \frac{0.14}{0.098} \approx 1.42857 \, \text{m} \]

### Step 7: Round to appropriate significant figures
Rounding to four significant figures, we get:

\[ h \approx 0.1429 \, \text{m} \]

### Final Answer
The rise of water inside the capillary tube is approximately **0.1429 m** or **14.29 cm**.

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