A horizontal disc rotates freely with angular velocity `omega` about a vertical axes through its centre. A ring having the same mass and radius as the disc, is now gently placed coaxially on the disc. After some time, the two rotate with a common angular velocity. then.

Options

A. no friction exists between te disc and the ring
B. the angular momentum of the system is conserved
C. the final common angular velocity is `(1)/(2)omega`
D. all of the above

Explanation

To solve the problem step by step, we will analyze the situation involving a rotating disc and a ring placed on it.

### Step 1: Understand the Initial Conditions
- A horizontal disc is rotating with an angular velocity \( \omega \) about a vertical axis through its center.
- A ring, having the same mass \( m \) and radius \( r \) as the disc, is gently placed coaxially on the disc.

**Hint:** Identify the initial angular momentum of the system before the ring is placed.

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