A body covers a distance of L along a semicircular path. Then the ratio of distance to displacement is

Options

A. `(2L)/(pi)`
B. `(L )/(pi )`
C. `(pi )/(2L)`
D. `(pi )/(2)`

Explanation

To solve the problem of finding the ratio of distance to displacement when a body covers a distance of L along a semicircular path, we can follow these steps:

### Step 1: Understand the Definitions
- **Distance** is the total length of the path traveled by the body.
- **Displacement** is the shortest straight-line distance between the initial and final positions of the body.

### Step 2: Analyze the Semicircular Path
- The body moves along a semicircular path from point A to point B.
- The distance covered along this path is given as L.

### Step 3: Calculate the Distance
- Since the body travels along the semicircular path, the distance covered is simply L.

**Distance (D) = L**

### Step 4: Calculate the Displacement
- The displacement is the straight-line distance from the starting point A to the endpoint B.
- For a semicircular path, if the radius of the semicircle is r, the displacement can be calculated as the diameter of the semicircle.

**Displacement (S) = 2r**

### Step 5: Relate the Radius to the Distance
- The length of the semicircular path (which is the distance L) can be expressed in terms of the radius r:

\[ L = \pi r \quad \text{(Circumference of a full circle is } 2\pi r \text{, so for semicircle it's } \pi r\text{)} \]

- From this, we can express the radius r in terms of L:

\[ r = \frac{L}{\pi} \]

### Step 6: Substitute the Radius into the Displacement Formula
- Now, substituting the value of r into the displacement formula:

\[ S = 2r = 2 \left(\frac{L}{\pi}\right) = \frac{2L}{\pi} \]

### Step 7: Calculate the Ratio of Distance to Displacement
- Now we can find the ratio of distance to displacement:

\[ \text{Ratio} = \frac{\text{Distance}}{\text{Displacement}} = \frac{L}{\frac{2L}{\pi}} = \frac{L \cdot \pi}{2L} = \frac{\pi}{2} \]

### Final Answer
The ratio of distance to displacement when a body covers a distance of L along a semicircular path is:

\[ \text{Ratio} = \frac{\pi}{2} \]

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