**Correct Option: C. Centripetal force** ### Detailed Explanation: When an object moves in a circular path at a constant speed, it is undergoing uniform circular motion. The key aspect of this motion is that, although the speed remains constant, the direction of the object's velocity is continuously changing. This change in direction means that the object is accelerating, even if its speed does not change. 1. **Understanding Centripetal Force**: - Centripetal force is the net force that acts on an object moving in a circular path, directed towards the center of the circle. This force is essential for maintaining circular motion. Without it, the object would move off in a straight line due to inertia, as described by Newton's first law of motion. - The formula for centripetal force (\(F_c\)) can be expressed as: \[ F_c = \frac{mv^2}{r} \] where: - \(m\) is the mass of the object, - \(v\) is the tangential speed of the object, - \(r\) is the radius of the circular path. 2. **Why Centripetal Force is the Correct Answer**: - Centripetal force is not a separate force in itself but rather the net force resulting from other forces (like tension, gravity, or friction) that act towards the center of the circular path. It is this net inward force that keeps the object moving in a circle. - For example, in the case of a car turning on a flat road, the frictional force between the tires and the road provides the necessary centripetal force to keep the car moving in a circular path. ### Why the Other Options are Incorrect: - **A. Gravitational force**: - Gravitational force acts between two masses and is directed towards the center of the Earth (or another massive body). While it can contribute to centripetal force (like in the case of a satellite orbiting Earth), it is not the primary force responsible for circular motion in all scenarios. For example, a car turning on a flat road relies on friction, not gravity, to maintain its circular path. - **B. Frictional force**: - Frictional force can provide the necessary centripetal force in some cases (like a car turning on a road), but it is not the only force that can act as centripetal force. In scenarios like a satellite in orbit, there is no friction, yet centripetal force is still present due to gravitational attraction. Thus, while friction can be a source of centripetal force, it is not the primary force in all circular motion contexts. - **D. Normal force**: - The normal force acts perpendicular to the surface of contact and is responsible for supporting the weight of an object. In some cases, it can contribute to the centripetal force (like a roller coaster at the top of a loop), but it does not act towards the center of the circular path in all scenarios. Therefore, it cannot be considered the primary force for circular motion. ### Summary of Key Points: - Centripetal force is the net force that keeps an object moving in a circular path, directed towards the center. - It is calculated using the formula \(F_c = \frac{mv^2}{r}\). - Other forces (like gravitational and frictional forces) can provide centripetal force but are not the primary force in all cases. - Understanding the role of centripetal force is crucial for analyzing circular motion in various physical contexts.