The magnet of a vibration magnetometer is heated so as to reduce its magnetic moment by `19%`. By doing this the period time of the magnetometer will

Options

A. increase by 11%
B. decrease by 19%
C. increase by 19%
D. decrease by 11%

Answer

To solve the problem, we need to analyze how the magnetic moment of a vibration magnetometer affects its time period when the magnetic moment is reduced by 19%.

### Step-by-Step Solution:

1. **Understanding the Formula**:
The time period \( T \) of a vibration magnetometer is given by the formula:
\[ T = 2\pi \sqrt{\frac{I}{MB}} \]
where \( I \) is the moment of inertia, \( M \) is the magnetic moment, and \( B \) is the magnetic field. For our analysis, we will focus on the relationship between the time period and the magnetic moment.

2. **Inversely Proportional Relationship**:
From the formula, we can see that the time period \( T \) is inversely proportional to the magnetic moment \( M \). This means that if the magnetic moment decreases, the time period increases.

3. **Calculating the New Magnetic Moment**:
The problem states that the magnetic moment is reduced by 19%. If we assume the initial magnetic moment \( M \) is 100 (for simplicity), the new magnetic moment \( M' \) after the reduction will be:
\[ M' = M - 0.19M = 100 - 19 = 81 \]

4. **Setting Up the Ratio of Time Periods**:
The ratio of the original time period \( T \) to the new time period \( T' \) can be expressed as:
\[ \frac{T}{T'} = \sqrt{\frac{M'}{M}} = \sqrt{\frac{81}{100}} = \sqrt{0.81} = \frac{9}{10} \]

5. **Finding the New Time Period**:
Rearranging the ratio gives us:
\[ T' = \frac{10}{9} T \]
This indicates that the new time period \( T' \) is greater than the original time period \( T \).

6. **Calculating the Percentage Increase**:
To find the percentage increase in the time period:
\[ \text{Percentage Increase} = \left( \frac{T' - T}{T} \right) \times 100 = \left( \frac{\frac{10}{9}T - T}{T} \right) \times 100 = \left( \frac{10 - 9}{9} \right) \times 100 = \frac{1}{9} \times 100 \approx 11.11\% \]
Therefore, the time period increases by approximately 11%.

7. **Conclusion**:
The time period of the magnetometer will increase by approximately 11%.

### Final Answer:
The time period of the magnetometer will increase by 11%.