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) lt T_(2)`
B. `T_(1) gt T_(2)`
C. `T_(1)=T_(2)`
D. `T_(2)=oo`

Explanation

To solve the problem, we need to analyze the situation of two bar magnets with different magnetic moments and how their arrangement affects the time period of oscillation.

### Step-by-Step Solution:

1. **Understanding the Initial Configuration:**
- We have two bar magnets with magnetic moments \( M \) and \( 2M \).
- They are placed such that their similar poles (both south or both north) are on the same side.
- This configuration leads to a net magnetic moment that is the sum of the two magnetic moments since they are aligned in the same direction.

2. **Calculating the Effective Magnetic Moment:**
- The effective magnetic moment \( M_{eff} \) when both similar poles are together is:
\[ M_{eff} = M + 2M = 3M \]

3. **Time Period of Oscillation (Initial Case):**
- The time period \( T_1 \) of oscillation for a bar magnet in a magnetic field is given by:
\[ T = 2\pi \sqrt{\frac{I}{M_{eff} H}} \]
- Substituting \( M_{eff} \):
\[ T_1 = 2\pi \sqrt{\frac{I}{3MH}} \]

4. **Reversing the Polarity of One Magnet:**
- When the polarity of the magnet with magnetic moment \( 2M \) is reversed, the effective magnetic moment becomes:
\[ M_{eff}' = 2M - M = M \]

5. **Time Period of Oscillation (After Reversing Polarity):**
- The new time period \( T_2 \) is given by:
\[ T_2 = 2\pi \sqrt{\frac{I}{M H}} \]

6. **Comparing the Time Periods:**
- We can compare \( T_1 \) and \( T_2 \):
- From the expressions, we see that \( T_1 \) involves \( 3M \) in the denominator, while \( T_2 \) involves \( M \).
- Since \( 3M > M \), it follows that:
\[ T_2 > T_1 \]

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