A thin uniform rod of mass 'M' and ength 'L' is rotating about a perpendicular axis passing through its centre with a constant angular velocity `'omega '.` Two objects each of mass `(M)/(3)` are attached gently to the two ends of the rod. The rod will now rotate with an angular velocity of

Options

A. `1/3 omega`
B. `1/7 omega`
C. `1/6 omega`
D. `1/2 omega`

Explanation

To solve the problem, we will use the principle of conservation of angular momentum. The angular momentum before and after the objects are attached to the rod must be equal since there are no external torques acting on the system.

### Step-by-step Solution:

1. **Identify Initial Conditions:**
- The initial angular velocity of the rod is given as \( \omega \).
- The mass of the rod is \( M \) and its length is \( L \).

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