A bar magnet is oscillating in the earth's magnetic field with a time period `T`. If the mass is increased four times, then its time period will be:

Explanation

To solve the problem, we need to analyze how the time period of a bar magnet oscillating in a magnetic field changes when its mass is increased.

### Step-by-Step Solution:

1. **Understanding the Time Period of a Bar Magnet**:
The time period \( T \) of a bar magnet oscillating in a magnetic field is given by the formula:
\[ T \propto \sqrt{\frac{I}{m}} \]
where \( I \) is the moment of inertia and \( m \) is the mass of the magnet.

2. **Moment of Inertia of a Bar Magnet**:
For a bar magnet, the moment of inertia \( I \) about its center is given by:
\[ I = \frac{ml^2}{3} \]
However, for oscillations, we can consider the effective moment of inertia in terms of the mass and length.

3. **Effect of Increasing Mass**:
If the mass of the bar magnet is increased four times, we can denote the new mass as:
\[ m' = 4m \]

4. **New Time Period Calculation**:
The new time period \( T' \) can be expressed in terms of the original time period \( T \):
\[ T' \propto \sqrt{\frac{I}{m'}} \]
Substituting \( m' = 4m \):
\[ T' \propto \sqrt{\frac{I}{4m}} = \sqrt{\frac{1}{4}} \cdot \sqrt{\frac{I}{m}} = \frac{1}{2} \sqrt{\frac{I}{m}} \]

5. **Relating New Time Period to Original**:
Since \( T \propto \sqrt{\frac{I}{m}} \), we can write:
\[ T' = 2T \]

6. **Conclusion**:
Therefore, when the mass of the bar magnet is increased four times, the new time period \( T' \) becomes:
\[ T' = 2T \]

### Final Answer:
The new time period will be \( 2T \).