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 of how high water will rise in a capillary tube inclined at an angle of 60 degrees with the vertical, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We know that water rises to a height of 2 cm in a vertical capillary tube. When the tube is inclined at an angle of 60 degrees with the vertical, we need to find the new height (H') that the water will rise to along the inclined tube.

2. **Identify the Relationship**: When the tube is inclined, the vertical height (h) that the water rises is related to the length of the water column (H') in the inclined tube by the cosine of the angle of inclination. This can be expressed mathematically as:
\[ h = H' \cdot \cos(\theta) \]
where \( h \) is the vertical height (2 cm), \( H' \) is the length of the water column in the inclined tube, and \( \theta \) is the angle of inclination (60 degrees).

3. **Substitute Known Values**: We know that \( h = 2 \) cm and \( \theta = 60^\circ \). The cosine of 60 degrees is:
\[ \cos(60^\circ) = \frac{1}{2} \]

4. **Rearranging the Equation**: We can rearrange the equation to solve for \( H' \):
\[ H' = \frac{h}{\cos(\theta)} = \frac{2 \text{ cm}}{\cos(60^\circ)} \]

5. **Calculate \( H' \)**: Substituting the value of \( \cos(60^\circ) \):
\[ H' = \frac{2 \text{ cm}}{\frac{1}{2}} = 2 \text{ cm} \times 2 = 4 \text{ cm} \]

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

### Conclusion:
The water will rise to a length of **4 cm** in the inclined capillary tube.

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