What will be the length of mercury column in a barometer tube when the atmospheric pressure is x cm of mercury and the tube is inclined at an angle `phi` with the vertical direction ?

Options

A. `(x)/(sin phi)`
B. `(x)/(cos phi)`
C. `(x)/(tan phi)`
D. x

Explanation

To find the length of the mercury column in a barometer tube inclined at an angle \( \phi \) with the vertical when the atmospheric pressure is \( x \) cm of mercury, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a barometer tube that is inclined at an angle \( \phi \) with respect to the vertical.
- The height of the mercury column due to atmospheric pressure is \( x \) cm.

2. **Identifying the Components**:
- When the tube is inclined, the length of the mercury column \( L \) can be related to the vertical height of the mercury column. The vertical height of the mercury column is \( x \) cm.

3. **Using Trigonometry**:
- In the inclined position, we can use trigonometric relationships. The vertical height \( x \) can be expressed in terms of the length \( L \) of the mercury column and the angle \( \phi \):
\[ x = L \cos(\phi) \]
- Here, \( L \) is the hypotenuse (the length of the mercury column) and \( x \) is the adjacent side (the vertical height of the mercury column).

4. **Solving for Length \( L \)**:
- Rearranging the equation gives:
\[ L = \frac{x}{\cos(\phi)} \]
- This can also be expressed as:
\[ L = x \sec(\phi) \]

5. **Conclusion**:
- Therefore, the length of the mercury column in the barometer tube when inclined at an angle \( \phi \) with the vertical is:
\[ L = x \sec(\phi) \]

### Final Answer:
The length of the mercury column in the barometer tube is \( L = x \sec(\phi) \).