A vibration magnetometer is placed at the south pole, then the time period will be

Options

A. zero
B. infinity
C. same as at magnetic equator
D. same as at any other place on earth

Answer

To solve the problem of determining the time period of a vibration magnetometer placed at the South Pole, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Time Period**:
The time period \( T \) of a vibration magnetometer is given by the formula:
\[ T = 2\pi \sqrt{\frac{I}{M B_H}} \]
where:
- \( I \) is the moment of inertia of the magnet,
- \( M \) is the magnetic moment of the magnet,
- \( B_H \) is the horizontal component of the Earth's magnetic field.

2. **Analyze the Situation at the South Pole**:
At the South Pole, the magnetic field lines point vertically downwards. This means that the horizontal component of the magnetic field \( B_H \) is effectively zero:
\[ B_H = 0 \]

3. **Substituting \( B_H \) into the Formula**:
Substituting \( B_H = 0 \) into the time period formula, we get:
\[ T = 2\pi \sqrt{\frac{I}{M \cdot 0}} \]

4. **Evaluate the Expression**:
Since \( B_H = 0 \), the term \( M \cdot B_H \) becomes zero, leading to:
\[ T = 2\pi \sqrt{\frac{I}{0}} \rightarrow T = \infty \]
This indicates that the time period becomes infinite.

5. **Conclusion**:
Therefore, the time period of the vibration magnetometer placed at the South Pole is infinite.

### Final Answer:
The correct option is **B: Infinity**.