Water rises in a vertical capillary tube up to a height of 2.0 cm. If the tube is inclined at an angle of `60^@` with the vertical, then up to what length the water will rise in the tube ?

Options

A. 2.0 cm
B. 4. 0 cm
C. 6. 0 cm
D. 8. 0 cm

Answer

To solve the problem, we need to determine the length of the water column in the capillary tube when it is inclined at an angle of 60 degrees with the vertical. The initial height of the water column when the tube is vertical is given as 2 cm.

### Step-by-Step Solution:

1. **Understand the Problem**:
- When the tube is vertical, the water rises to a height of 2 cm due to capillary action.
- When the tube is inclined at an angle of 60 degrees with the vertical, we need to find the new length of the water column along the inclined tube.

2. **Visualizing the Geometry**:
- When the tube is inclined, the height (h) of the water column remains the same (2 cm) because the pressure difference that caused the rise is unchanged.
- The length of the water column (L) in the inclined tube can be related to the height using trigonometric functions.

3. **Using Trigonometry**:
- The relationship between the height (h), the length of the water column (L), and the angle (θ) is given by:
\[ h = L \cdot \cos(θ) \]
- Here, \( h = 2 \, \text{cm} \) and \( θ = 60^\circ \).

4. **Substituting the Values**:
- We can rearrange the formula to solve for L:
\[ L = \frac{h}{\cos(θ)} \]
- Substitute the known values:
\[ L = \frac{2 \, \text{cm}}{\cos(60^\circ)} \]

5. **Calculating Cosine**:
- We know that \( \cos(60^\circ) = \frac{1}{2} \).
- Therefore:
\[ L = \frac{2 \, \text{cm}}{\frac{1}{2}} = 2 \, \text{cm} \times 2 = 4 \, \text{cm} \]

6. **Final Answer**:
- The length of the water column in the inclined tube is **4 cm**.