Water rises to a height of `2 cm` in a capillary tube. If the tube is tilted `60^@` from the vertical, water will rise in the tube to a length of

Options

A. `4.0cm`
B. `2.0cm`
C. `1.0cm`
D. water will not rise at all

Explanation

To solve the problem of how high water will rise in a capillary tube tilted at an angle of \(60^\circ\) from the vertical, we can follow these steps:

### Step 1: Understand the Initial Condition
In the vertical position, the water rises to a height of \(2 \, \text{cm}\). This height is the vertical height of the water column in the capillary tube.

### Step 2: Identify the Effect of Tilting
When the capillary tube is tilted at an angle of \(60^\circ\), the vertical height of the water column does not change. However, the length of the water column in the tube will change because the tube is no longer vertical.

### Step 3: Relate the Vertical Height to the Length of the Water Column
To find the length of the water column (\(L\)) in the tilted tube, we can use the relationship between the vertical height (\(h\)) and the length of the water column in the tilted position. The relationship is given by:
\[ L = \frac{h}{\cos(\theta)} \]
where \(h\) is the vertical height of the water column and \(\theta\) is the angle of tilt.

### Step 4: Substitute the Values
In our case, \(h = 2 \, \text{cm}\) and \(\theta = 60^\circ\). We know that:
\[ \cos(60^\circ) = \frac{1}{2} \]
Now substituting the values into the equation:
\[ L = \frac{2 \, \text{cm}}{\cos(60^\circ)} = \frac{2 \, \text{cm}}{\frac{1}{2}} = 2 \, \text{cm} \times 2 = 4 \, \text{cm} \]

### Step 5: Conclusion
Thus, when the capillary tube is tilted at an angle of \(60^\circ\) from the vertical, the water will rise to a length of \(4 \, \text{cm}\) in the tube.

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