If a particle complete one and half revolution along the circumference of a circle then its angular displacement is -

Options

A. 0
B. `pi`
C. `2pi`
D. `3pi`

Answer

To solve the problem of finding the angular displacement of a particle that completes one and a half revolutions along the circumference of a circle, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the concept of angular displacement**: Angular displacement is the angle through which a point or line has been rotated in a specified sense about a specified axis. For one complete revolution, the angular displacement is \(2\pi\) radians.

2. **Calculate the angular displacement for one revolution**:
- For one complete revolution, the angular displacement is:
\[ \text{Angular Displacement for 1 revolution} = 2\pi \text{ radians} \]

3. **Calculate the angular displacement for one and a half revolutions**:
- One and a half revolutions can be expressed as:
\[ 1.5 \text{ revolutions} = \frac{3}{2} \text{ revolutions} \]
- Therefore, the angular displacement for one and a half revolutions is:
\[ \text{Angular Displacement} = 2\pi \times \frac{3}{2} = 3\pi \text{ radians} \]

4. **Conclusion**: The angular displacement of the particle after completing one and a half revolutions is:
\[ \text{Angular Displacement} = 3\pi \text{ radians} \]

### Final Answer:
The angular displacement is \(3\pi\) radians.

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