A particle is moving on a cicular path of radius 'R' . As it moves through an angular displacement `theta`, its linear displacement will be :

Options

A. `R sin theta`
B. `2R cos theta//2`
C. `2R sin theta//2`
D. `R cos theta`

Explanation

To find the linear displacement of a particle moving along a circular path with a radius \( R \) after an angular displacement \( \theta \), we can follow these steps:

### Step 1: Understand the Circular Motion
The particle moves along the circumference of a circle with radius \( R \). The angular displacement \( \theta \) is measured in radians.

### Step 2: Calculate the Arc Length
The linear displacement \( s \) (arc length) corresponding to the angular displacement \( \theta \) is given by the formula:
\[ s = R \cdot \theta \]
where:
- \( s \) is the linear displacement,
- \( R \) is the radius of the circular path,
- \( \theta \) is the angular displacement in radians.

### Step 3: Substitute the Values
If we substitute the values into the formula, we can express the linear displacement as:
\[ s = R \cdot \theta \]

### Conclusion
Thus, the linear displacement of the particle as it moves through an angular displacement \( \theta \) on a circular path of radius \( R \) is:
\[ s = R \theta \]