Water rises in a capillary tube to a height of 2.0cm. In another capillary tube whose radius is one third of it, how much the water will rise?

Explanation

To solve the problem, we will use the relationship between the height of liquid rise in a capillary tube and the radius of the tube. The formula we will use is:

\[ h_1 \cdot r_1 = h_2 \cdot r_2 \]

Where:
- \( h_1 \) = height of water rise in the first capillary tube
- \( r_1 \) = radius of the first capillary tube
- \( h_2 \) = height of water rise in the second capillary tube
- \( r_2 \) = radius of the second capillary tube

### Step-by-step Solution:

1. **Identify the given values:**
- Height of water rise in the first capillary tube, \( h_1 = 2 \, \text{cm} \)
- The radius of the second capillary tube is one third of the first, so \( r_2 = \frac{1}{3} r_1 \)

2. **Set up the equation using the capillary rise relation:**
\[ h_1 \cdot r_1 = h_2 \cdot r_2 \]

3. **Substitute the known values into the equation:**
\[ 2 \, \text{cm} \cdot r_1 = h_2 \cdot \left(\frac{1}{3} r_1\right) \]

4. **Simplify the equation:**
- Cancel \( r_1 \) from both sides (assuming \( r_1 \neq 0 \)):
\[ 2 = h_2 \cdot \frac{1}{3} \]

5. **Solve for \( h_2 \):**
\[ h_2 = 2 \cdot 3 = 6 \, \text{cm} \]

### Final Answer:
The height of water rise in the second capillary tube is \( h_2 = 6 \, \text{cm} \).