Circular Motion Statements – Detailed Solution

Circular Motion: Statement-Based Problem

Question: Consider an object moving in uniform circular motion. Which of the following statements are correct?

1. Statement A: The net force acting on the object does zero work.
2. Statement B: The object's speed remains constant.
3. Statement C: The centripetal acceleration is always directed toward the center of the circle and is perpendicular to the velocity at every point.
4. Statement D: The momentum of the object remains constant in both magnitude and direction.

Choose the option that correctly lists all the true statements:

• (1) A, B, and C only
• (2) B and D only
• (3) A, B, and D only
• (4) All of the above

Select the Correct Option

(1) A, B, and C only

(2) B and D only

(3) A, B, and D only

(4) All of the above

Step-by-Step Explanation

1. Statement A: The net force on an object in uniform circular motion is the centripetal force, which is always directed toward the center of the circle. Since this force is perpendicular to the instantaneous displacement (and velocity), it does no work on the object. Thus, Statement A is true.
2. Statement B: In uniform circular motion, the magnitude of the velocity (i.e. speed) remains constant, though its direction continuously changes. Therefore, Statement B is true.
3. Statement C: The centripetal acceleration is defined by \[ a_c = \frac{v^2}{R}, \] and is always directed toward the center of the circular path. Since the velocity is tangent to the circle, the centripetal acceleration is perpendicular to the velocity vector. Thus, Statement C is true.
4. Statement D: Although the magnitude of the momentum \(p = mv\) remains constant (because \(m\) and \(v\) are constant), the momentum is a vector quantity whose direction changes continuously as the object travels around the circle. Therefore, the momentum is not constant in direction. Statement D is false.
5. Final Conclusion: The true statements are A, B, and C. The correct choice is Option (1): A, B, and C only.