The lower end of a capillary tube is at a depth of `12 cm` and water rises `3 cm` in it. The mouth pressure required to blow an air bubble at the lower end will be `x cm` of water column, where `x` is

Options

A. `12`
B. `15`
C. `3`
D. `9`

Explanation

To solve the problem, we need to determine the mouth pressure required to blow an air bubble at the lower end of a capillary tube, given that the lower end is at a depth of 12 cm and water rises 3 cm in the tube.

### Step-by-step Solution:

1. **Understand the Setup**:
- The lower end of the capillary tube is at a depth of 12 cm.
- Water rises 3 cm in the tube, meaning the height of the water column above the lower end is 3 cm.

2. **Identify Total Depth**:
- The total height of the water column that we need to consider for pressure calculations is the depth of the lower end plus the height of the water rise.
- Total height (h) = Depth of the lower end + Height of water rise = 12 cm + 3 cm = 15 cm.

3. **Pressure Calculation**:
- The pressure at the lower end of the capillary tube (where the bubble is to be blown) can be expressed in terms of the height of the water column.
- The pressure at this point (P2) is equal to the atmospheric pressure (P0) plus the pressure due to the height of the water column (h).
- Therefore, P2 = P0 + h * ρ * g, where ρ is the density of water and g is the acceleration due to gravity.

4. **Pressure Required to Blow the Bubble**:
- The pressure required to blow the bubble (P_required) is the difference between the pressure at the lower end (P2) and the atmospheric pressure (P0).
- Thus, P_required = P2 - P0 = (P0 + h * ρ * g) - P0 = h * ρ * g.

5. **Substituting Values**:
- Since we are interested in the height of the water column equivalent to this pressure, we can express it simply as the height h.
- From our earlier calculation, h = 15 cm.

6. **Conclusion**:
- Therefore, the mouth pressure required to blow an air bubble at the lower end of the capillary tube is equivalent to a height of 15 cm of water column.

### Final Answer:
The value of x is 15 cm.