Correct Option
When a spherical body moves in a circular path with a uniform angular velocity (ω), it undergoes uniform circular motion. Although the magnitude of its velocity (speed) remains constant, the direction of its velocity continuously changes. This change in direction implies that the body is accelerating.
This acceleration is known as centripetal or radial acceleration. It is always directed towards the center of the circular path. The magnitude of this acceleration is given by the formula a = ω²r, where 'r' is the radius of the circular path. Therefore, the body has a radial acceleration ω²r directed toward the center of the path.
Incorrect Options
1) The body has no acceleration: This statement is incorrect. In uniform circular motion, even though the speed is constant, the continuous change in the direction of velocity results in a non-zero centripetal (radial) acceleration.
3) The body has a radial acceleration 2/5 ω²r directed away from the centre of the path: This statement is incorrect on two counts. The magnitude of the radial acceleration is ω²r, not 2/5 ω²r. Furthermore, the centripetal acceleration is always directed towards the center of the path, not away from it.
4) The body has an acceleration ω² tangential to its path: This statement is incorrect. Tangential acceleration occurs when there is a change in the speed of the body. In uniform circular motion, the speed is constant, hence there is no tangential acceleration. The acceleration present is radial (centripetal).