A glass marble moves from one end of a semiciecular arc of radius R to the other end of the arc, The ratio of distance travelled by the marble to its displacement is

Options

A. `pi//R`
B. `R//pi`
C. `2pi`
D. `pi//2`

Explanation

To solve the problem, we need to find the ratio of the distance traveled by a glass marble moving along a semicircular arc to its displacement.

### Step-by-Step Solution:

1. **Understanding the Path**:
The marble moves along a semicircular arc from one end to the other. The radius of the semicircular arc is given as \( R \).

2. **Calculating the Distance Traveled**:
The distance traveled by the marble is the length of the semicircular arc. The formula for the length of a semicircle is:
\[ \text{Distance} = \pi R \]

3. **Calculating the Displacement**:
Displacement is defined as the shortest distance between the initial and final points. For a semicircular path, the initial and final points are the endpoints of the diameter. The length of the diameter is:
\[ \text{Displacement} = 2R \]

4. **Finding the Ratio**:
Now, we can find the ratio of the distance traveled to the displacement:
\[ \text{Ratio} = \frac{\text{Distance}}{\text{Displacement}} = \frac{\pi R}{2R} \]
Simplifying this gives:
\[ \text{Ratio} = \frac{\pi}{2} \]

5. **Final Answer**:
Therefore, the ratio of the distance traveled by the marble to its displacement is:
\[ \frac{\pi}{2} \]