Assuming the xylem tissues through which water rises from root to the branches in a tree to be of uniform cross-section find the maximum radius of xylem tube in a `10m` high coconut tree so that water can rise to the top.
(Surface tension of water`=0.1(N)/(m)`, Angle of contact of water with xylem tube`=60^@`)

Options

A. `2 mum`
B. `3 mu m`
C. `5 mu m`
D. `1 mu m`

Explanation

To solve the problem of finding the maximum radius of the xylem tube in a 10m high coconut tree, we can use the formula for the height of liquid rise in a capillary tube. The formula is given by:

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

Where:
- \( h \) = height of the liquid column (10 m)
- \( s \) = surface tension of the liquid (0.1 N/m)
- \( \theta \) = angle of contact (60°)
- \( \rho \) = density of water (approximately \( 1000 \, \text{kg/m}^3 \))
- \( g \) = acceleration due to gravity (approximately \( 10 \, \text{m/s}^2 \))
- \( r \) = radius of the xylem tube (unknown)

### Step-by-Step Solution:

1. **Identify the known values:**
- Height \( h = 10 \, \text{m} \)
- Surface tension \( s = 0.1 \, \text{N/m} \)
- Angle of contact \( \theta = 60° \)
- Density of water \( \rho = 1000 \, \text{kg/m}^3 \)
- Acceleration due to gravity \( g = 10 \, \text{m/s}^2 \)

2. **Calculate \( \cos \theta \):**
\[ \cos 60° = \frac{1}{2} \]

3. **Substitute the known values into the formula:**
\[ 10 = \frac{2 \times 0.1 \times \frac{1}{2}}{1000 \times 10 \times r} \]

4. **Simplify the equation:**
\[ 10 = \frac{0.1}{10000 r} \]
\[ 10 = \frac{1}{100000 r} \]

5. **Rearranging to solve for \( r \):**
\[ 10 \times 100000 r = 1 \]
\[ r = \frac{1}{1000000} = 10^{-6} \, \text{m} \]

6. **Convert the radius to micrometers:**
\[ r = 10^{-6} \, \text{m} = 1 \, \mu m \]

### Final Answer:
The maximum radius of the xylem tube is \( 1 \, \mu m \) or \( 10^{-6} \, \text{m} \).

---