A particle is movingin circular path of radius 7 cm. Find the ratio of its displacement to the distance covered after the completion of a half

Explanation

To solve the problem of finding the ratio of displacement to distance covered by a particle moving in a circular path of radius 7 cm after completing half the circle, follow these steps:

### Step-by-Step Solution:

1. **Understand the Circular Path**:
The particle is moving along a circular path with a radius (r) of 7 cm.

2. **Calculate the Distance Covered**:
When the particle completes half of the circular path, it travels along a semicircular arc. The formula for the circumference (C) of a full circle is given by:
\[ C = 2\pi r \]
For half of the circle (semicircle), the distance (s) covered is:
\[ s = \frac{C}{2} = \pi r \]
Substituting the radius:
\[ s = \pi \times 7 \text{ cm} = 7\pi \text{ cm} \]

3. **Calculate the Displacement**:
Displacement is defined as the shortest distance between the initial and final points. After moving halfway around the circle, the particle moves from point A to point B, which is directly across the diameter of the circle. The diameter (d) can be calculated as:
\[ d = 2r \]
Substituting the radius:
\[ d = 2 \times 7 \text{ cm} = 14 \text{ cm} \]

4. **Find the Ratio of Displacement to Distance**:
Now, we can find the ratio of displacement (d) to distance (s):
\[ \text{Ratio} = \frac{\text{Displacement}}{\text{Distance}} = \frac{d}{s} = \frac{14 \text{ cm}}{7\pi \text{ cm}} \]
Simplifying this gives:
\[ \text{Ratio} = \frac{14}{7\pi} = \frac{2}{\pi} \]

5. **Substituting the Value of \(\pi\)**:
If we take \(\pi \approx \frac{22}{7}\) for calculation:
\[ \text{Ratio} = \frac{2}{\frac{22}{7}} = \frac{2 \times 7}{22} = \frac{14}{22} = \frac{7}{11} \]

### Final Answer:
The ratio of displacement to distance covered after the completion of half the circle is:
\[ \frac{7}{11} \]