A uniform disc is rotating at a constant speed in a vertical plane about a fixed horizontal axis passing through the centre of the disc. A piece of the disc at the instant when it is at a horizontal level with the centre of the disc and moving upward . Then about the fixed axis, the angular speed of the remaining disc is

Options

A. remains unchanged
B. decreases
C. increase
D. initially increases and later decreases

Answer

To solve the problem, we need to analyze the situation of a uniform disc rotating about a fixed horizontal axis and understand the implications of a piece of the disc moving upward.

### Step-by-step Solution:

1. **Understanding the System**:
- We have a uniform disc rotating in a vertical plane about a fixed horizontal axis passing through its center.
- The disc is rotating at a constant angular speed, denoted as \( \omega \).

2. **Identifying the Piece of the Disc**:
- At a certain instant, a piece of the disc is at the horizontal level with the center of the disc and is moving upward.
- This piece is part of the rotating disc, and its motion is influenced by the rotation of the entire disc.

3. **Constant Angular Speed**:
- Since the disc is rotating at a constant speed, this means that the angular speed \( \omega \) of the entire disc does not change over time.
- The angular speed is defined as the rate of change of angular displacement with respect to time.

4. **Effect of the Piece Moving Upward**:
- The upward motion of the piece does not affect the overall angular speed of the remaining part of the disc.
- This is because the angular speed \( \omega \) is a scalar quantity that remains constant as long as the disc is rotating uniformly.

5. **Conclusion**:
- Therefore, the angular speed of the remaining disc, after the piece moves upward, remains unchanged.
- The angular speed of the remaining disc is still \( \omega \).

### Final Answer:
The angular speed of the remaining disc is \( \omega \).