Two bar magnets having same geometry with magnetic moments M and 2M, are firstly placed in such a way what their similar poles are same side then its time period of oscillation is `T_1`. Now the polarity of one of the magnet is reversed then time period of oscillation will be:-

Options

A. `T_(1)ltT_(2)`
B. `T_(1)gtT_(2)`
C. `T_(1)=T_(2)`
D. `T_(1)=oo,T_(1)=0`

Explanation

To solve the problem, we need to analyze the situation involving two bar magnets with magnetic moments \( M \) and \( 2M \). We will determine the time period of oscillation in two scenarios: when the magnets are aligned with similar poles together and when the polarity of one magnet is reversed.

### Step-by-Step Solution:

1. **Understanding the Initial Configuration:**
- We have two bar magnets with magnetic moments \( M \) and \( 2M \).
- When they are placed with similar poles together, they repel each other.

2. **Calculating the Effective Magnetic Moment:**
- The effective magnetic moment \( M_{\text{eff}} \) when similar poles are together can be calculated as:
\[ M_{\text{eff}} = M_1 + M_2 = M + 2M = 3M \]

3. **Using the Formula for Time Period:**
- The time period \( T \) of oscillation for a magnetic dipole in a magnetic field is given by:
\[ T = 2\pi \sqrt{\frac{I}{M_{\text{eff}} B}} \]
- Here, \( I \) is the moment of inertia, \( M_{\text{eff}} \) is the effective magnetic moment, and \( B \) is the magnetic field.

4. **Time Period in the Initial Configuration:**
- Let the time period in the initial configuration (similar poles together) be \( T_1 \):
\[ T_1 = 2\pi \sqrt{\frac{I}{3MB}} \]

5. **Reversing the Polarity of One Magnet:**
- When the polarity of one magnet is reversed, the effective magnetic moment becomes:
\[ M_{\text{eff}} = M_1 - M_2 = M - 2M = -M \]
- However, we take the absolute value for the calculation, so:
\[ M_{\text{eff}} = 2M - M = M \]

6. **Calculating the New Time Period:**
- Let the new time period after reversing the polarity be \( T_2 \):
\[ T_2 = 2\pi \sqrt{\frac{I}{MB}} \]

7. **Comparing the Time Periods:**
- To find the relationship between the two time periods, we can compare \( T_2 \) and \( T_1 \):
\[ \frac{T_2}{T_1} = \frac{2\pi \sqrt{\frac{I}{MB}}}{2\pi \sqrt{\frac{I}{3MB}}} = \sqrt{\frac{3}{1}} = \sqrt{3} \]
- This shows that \( T_2 > T_1 \).

8. **Conclusion:**
- The new time period \( T_2 \) is greater than the initial time period \( T_1 \).

### Final Answer:
The time period of oscillation after reversing the polarity of one magnet will be greater than \( T_1 \).