Question

A particle moves in a circle of radius \( R \). In half the period of revolution its displacement and distance covered respectively are:

• A. \( 2R, \pi R \)
• B. \( 2\pi R, 2R \)
• C. \( R, 2R \)
• D. \( \pi R, \frac{R}{2} \)

Hint:

For circular motion, the displacement in half a revolution is equal to the diameter of the circle, and the distance covered is half the circumference.

Answer 1

The Correct Option is A

When a particle moves in a circular path, in half the period of revolution it covers a semi-circular path. Let’s consider the motion of the particle:
- The total distance covered by the particle in half the period is half the circumference of the circle.
Thus, the distance \( d \) covered is: \[ d = \pi R \] - The displacement, which is the straight-line distance between the initial and final position of the particle, is the diameter of the circle. Therefore, the displacement \( s \) is: \[ s = 2R \] Hence, the displacement is \( 2R \) and the distance covered is \( \pi R \).