Question

A particle is moving on a circular path of radius r. Its displacement after one revolution :

• A. \(2\pi r\)
• B. \(\pi r\)
• C. \(0 \ \text{(zero)}\)
• D. \(2r\)

Hint:

Always distinguish between distance and displacement: {Distance:} Total path length. Always positive or zero. Scalar. {Displacement:} Shortest distance between initial and final points (a straight line). Vector. Can be positive, negative, or zero. For any motion where the object returns to its starting point (like one full revolution on a circle, or a round trip), the total displacement is always zero, even if the distance traveled is non-zero.

Answer 1

The Correct Option is C

Concept: It's important to differentiate between distance and displacement.
Distance is the total length of the path traveled by an object. It is a scalar quantity.
Displacement is the shortest straight-line distance between the initial and final positions of an object. It is a vector quantity (meaning it has both magnitude and direction). Step 1: Visualize the motion A particle is moving on a circular path of radius \(r\). It completes one revolution. This means the particle starts at a certain point on the circle and, after moving along the circumference, returns to the exact same starting point. Step 2: Determine the initial and final positions Let the starting point of the particle on the circular path be point A. After one complete revolution, the particle comes back to point A. So, Initial Position = Point A Final Position = Point A Step 3: Calculate the displacement Displacement is defined as the change in position, or the shortest straight-line distance between the initial and final positions. Since the initial position and the final position are the same (Point A), the straight-line distance between them is zero. Displacement = Final Position - Initial Position If both are the same point, the vector difference is the zero vector, and its magnitude is 0. Therefore, the displacement of the particle after one complete revolution is 0 (zero). Step 4: Consider the distance traveled (for clarity, though not asked) The distance traveled in one revolution is the circumference of the circular path. Circumference of a circle with radius \(r\) is given by \(2\pi r\). So, the distance traveled would be \(2\pi r\). This corresponds to option (1), but the question asks for displacement. Option (2) \(\pi r\) is half the circumference (distance for half a revolution). Option (4) \(2r\) is the diameter (displacement if the particle moved from one end of a diameter to the other, i.e., half a revolution). The question specifically asks for {displacement}.