A particle is rotating in a circle of radius r. The distance traversed by it in completing half circle would be

The correct option is πr.

Step-by-step Explanation:

1. Understanding Distance:
Distance is the total length of the path traversed by a moving object. In this case, the particle moves along a circular path of radius $r$.

2. Circumference of a Circle:
The distance covered in one complete rotation is equal to the circumference of the circle. The circumference ($C$) is given by the formula:

$C=2\pi r$

3. Distance for a Half Circle:
Completing a half circle represents traveling half of the full circumference. Therefore, the distance traversed ($d$) is:

$d=\frac{C}{2}$

Substitute the value of $C$ into the equation:

$d=\frac{2\pi r}{2}$

Simplifying the expression by dividing the numerator and denominator by 2, we get:

$d=\pi r$

Thus, the distance traversed by the particle in completing a half circle is πr.