An object moves in a circular path with a constant speed. Which one of the following statements is correct ?

An object moving in a circular path at a constant speed undergoes uniform circular motion. The magnitude of centripetal acceleration (ac) is defined by the formula ac = v/r, where 'v' is the constant speed and 'r' is the radius of the path. This mathematical relationship indicates that centripetal acceleration is inversely proportional to the radius of the curve. Consequently, for a fixed speed, a 'gentle curve' with a larger radius results in a smaller centripetal acceleration compared to a 'sharp curve' with a smaller radius. While the speed remains constant, the velocity changes because the direction of motion is continuously altered by the centripetal force, which acts perpendicular to the velocity toward the center of rotation. Therefore, statement 1 is correct as it accurately describes the inverse relationship between the radius of curvature and the magnitude of acceleration.