Question

A particle moves in a circular path of radius r. In half the period of revolution its displacement and distance covered are.
\[\begin{align}
  & \text{A}\text{. }2r,\pi r \\
 & \text{B}\text{. }r,\pi r \\
 & \text{C}.\text{ }2r,2\pi r \\
 & \text{D}\text{. }r\sqrt{2},\pi r \\
\end{align}\]

Answer 1

Hint: We know that basically in circular motion the total displacement for half complete motion is the shortest distance between initial and final points that is diameter. And the distance covered is actual path travelled that is half the circumference.

Complete step by step answer:
The displacement of a particle for complete one revolution will be its diameter.
Hence displacement will be 2r where,
R is the radius of the circle.
The distance travelled by the particle for complete half revolution will be half the circumference.
Hence distance travelled will be \[\pi r\].

So, the correct answer is “Option A”.

Additional Information:
Distance or path length: it is the actual length travelled by the body between initial position and final position.
Distance is the scalar quantity because it has only magnitude and no direction. Distance covered is always positive or zero. The S.I unit of distance is m(metre).
Displacement: The displacement of the object is the change in position of an object in a fixed direction. It is the shortest path measured in the direction from initial point to final point. Displacement is the vector quantity and has both magnitude and direction. Displacement may be positive, negative or zero.
Characteristics of displacement: displacements have units of length.
The displacement of an object can be negative or zero.
Displacement is not dependent on the choice of the origin O of the position coordinates.
The actual distance travelled by the object is greater than or equal to the magnitude of displacement.

Note:
The displacement in circular motion will be 0 because displacement is the shortest path between initial and final position and in this case both the points coincide resulting in 0 displacement. And for distance travelled that is defined as actual path travelled which is the circumference of the circle.