A cyclist starts from the centre O of circular path of radius 10 m, covers the radius of circular path and reaches at point X on circumference, then cycles along the semi-circular path and reaches the point Y. If he takes 10 minutes to go from O to Y via X, then the net displacement and average speed of the cyclist would be

Options

A. `Zero, 10 ms^(-1)`
B. `10 m, ((1+ pi)/60)ms^(-1)`
C. `10 m, ((1+ pi)/6)ms^(-1)`
D. `10 m, ((1- pi)/60)ms^(-1)`

Answer

To solve the problem, we will follow these steps:

### Step 1: Identify the displacement
The cyclist starts from the center O of the circular path and reaches point Y on the circumference. The displacement is the straight-line distance from the starting point O to the final point Y.

- Given that the radius of the circular path is 10 m, the displacement from O to Y is equal to the radius of the circular path.

**Displacement = 10 m**

### Step 2: Calculate the total distance traveled
1. **Distance from O to X**:
The cyclist travels from the center O to point X on the circumference. This distance is equal to the radius of the circular path.
- Distance O to X = 10 m

2. **Distance from X to Y**:
The cyclist then travels along the semi-circular path from point X to point Y. The distance of a semi-circular path is half the circumference of the circle.
- Circumference of the circular path = 2πr = 2π(10 m) = 20π m
- Distance X to Y = (1/2) * Circumference = (1/2) * 20π = 10π m

3. **Total distance traveled**:
- Total distance = Distance O to X + Distance X to Y
- Total distance = 10 m + 10π m

### Step 3: Calculate the average speed
The average speed is defined as the total distance traveled divided by the total time taken.

1. **Total time taken**:
The cyclist takes 10 minutes to travel from O to Y. We need to convert this time into seconds for our calculations.
- Total time = 10 minutes = 10 × 60 seconds = 600 seconds

2. **Average speed calculation**:
- Average speed = Total distance / Total time
- Average speed = (10 + 10π) m / 600 s

### Final Results
- **Net Displacement**: 10 m
- **Average Speed**: (10 + 10π) / 600 m/s

### Summary of Results
- Displacement = 10 m
- Average Speed = (10 + 10π) / 600 m/s