A metallic circular disc having a circular hole at its centre rotates about an axis passing through its centre and perpendicular to its plane. When the disc is heated:

Options

A. its moment of inertia increases
B. its angular velocity increases.
C. its angular velocity decreases
D. its diameter increases.

Explanation

To solve the problem of what happens to a metallic circular disc with a hole at its center when it is heated and rotates about an axis through its center, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the System**: We have a metallic circular disc with a circular hole at its center. The disc rotates about an axis that is perpendicular to its plane and passes through its center.

2. **Effect of Heating**: When the disc is heated, it undergoes thermal expansion. This means that all parts of the disc, including the material around the hole, will expand.

3. **Expansion of the Disc**: As the disc heats up, the material expands outward. The particles of the disc will move away from the axis of rotation due to this expansion.

4. **Moment of Inertia**: The moment of inertia (I) of a rotating object depends on the mass distribution relative to the axis of rotation. Since the particles are moving farther from the axis as they expand, the moment of inertia of the disc will increase.

5. **Conservation of Angular Momentum**: In the absence of external torque, the angular momentum (L) of the system must remain constant. Angular momentum is given by the product of moment of inertia and angular velocity (L = Iω). Therefore, if the moment of inertia increases (I final > I initial), the angular velocity (ω) must decrease to keep the angular momentum constant.

6. **Conclusion**: After heating, the diameter of the disc increases due to thermal expansion, the moment of inertia increases, and consequently, the angular velocity decreases.

### Final Answers:
- The diameter of the disc increases.
- The moment of inertia increases.
- The angular velocity decreases.