The sap in tree rises in a system of capillaries of radius `2.5 xx 10^(-2) m`. The surface tension of the sap is `7.28 xx 10^(-2) N m^(-1)` and the angle of contact is `0^(@)`. The maximum height to which sap can rise in tree through capillarity action is `(rho_("sap")=10^(3) kg m^(-3))`

Options

A. 0.21 m
B. 0.59 m
C. 0.87 m
D. 0.91 m

Explanation

To find the maximum height to which sap can rise in a tree through capillary action, we can use the formula for capillary rise:

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

Where:
- \( h \) = height of the liquid column (in meters)
- \( s \) = surface tension of the liquid (in N/m)
- \( \theta \) = angle of contact (in degrees)
- \( \rho \) = density of the liquid (in kg/m³)
- \( r \) = radius of the capillary (in meters)
- \( g \) = acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \))

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Radius of the capillary, \( r = 2.5 \times 10^{-2} \, \text{m} \)
- Surface tension of the sap, \( s = 7.28 \times 10^{-2} \, \text{N/m} \)
- Angle of contact, \( \theta = 0^\circ \)
- Density of the sap, \( \rho = 10^3 \, \text{kg/m}^3 \)
- Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \)

2. **Calculate \( \cos \theta \):**
- Since \( \theta = 0^\circ \), we have:
\[ \cos 0 = 1 \]

3. **Substitute the Values into the Formula:**
\[ h = \frac{2 \times (7.28 \times 10^{-2}) \times 1}{(10^3) \times (2.5 \times 10^{-2}) \times (9.8)} \]

4. **Calculate the Numerator:**
\[ \text{Numerator} = 2 \times 7.28 \times 10^{-2} = 1.456 \times 10^{-1} \, \text{N/m} \]

5. **Calculate the Denominator:**
\[ \text{Denominator} = (10^3) \times (2.5 \times 10^{-2}) \times (9.8) = 10^3 \times 0.025 \times 9.8 = 245 \, \text{kg m}^{-2} \text{s}^{-2} \]

6. **Calculate the Height \( h \):**
\[ h = \frac{1.456 \times 10^{-1}}{245} \approx 5.94 \times 10^{-4} \, \text{m} \]

7. **Convert to Millimeters:**
\[ h \approx 0.594 \, \text{mm} \]

### Final Answer:
The maximum height to which sap can rise in the tree through capillary action is approximately \( 0.59 \, \text{mm} \).

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