Question

A body is moving along a circular path of radius r What will be the displacement of the body when it completes one revolution?
A. 0
B. 2r
C. $\pi r$
D. $2\pi r$

Answer 1

In this question we have been asked to calculate the displacement of the body when it completes one revolution along the circle with radius r. Now, we know that the displacement is the shortest distance in a straight line from the initial point or origin. Therefore, we shall make use of this concept to calculate the displacement of the given body.

Complete answer:
It is given that a body is moving along a circular path of radius r. Let us assume that the body started to travel from point A on the circle as shown in the figure below.

Now, it is given that the body completes one revolution along the circle. Let us say that the last position of the body is at point B. From the diagram, we can see that A and B are the same point of the circle. The line AB is also the shortest distance in a straight line joining the initial and final position of the body. We know that a straight line joining the final and initial positions is known as displacement
Now, it is given that the radius of the circle is ‘r’.
Therefore, the distance of line AB will be given by,
$d=0$
Therefore, the correct answer is option A.

Note:
The displacement is the distance between the initial and final position of a particle. Displacement is independent of the path taken to reach the final point. It means that if a particle reaches the final point through two different paths one being longer than the other, the displacement of the particle will still be the same irrespective of the distance travelled.