The correct option is **B. Centripetal force acts perpendicular to the velocity of the object and is directed towards the center of the circular path.** ### Detailed Explanation: 1. **Understanding Centripetal Force**: - Centripetal force is the net force that acts on an object moving in a circular path. It is always directed towards the center of the circle around which the object is moving. This force is crucial because it keeps the object from flying off in a straight line due to inertia (the tendency of an object to maintain its state of motion). 2. **Direction of Centripetal Force**: - In circular motion, the velocity of the object is tangential to the circular path. The centripetal force, however, acts at a right angle (perpendicular) to this velocity. This perpendicular nature of the force is what allows the object to change direction continuously while maintaining a constant speed, thus following a circular path. 3. **Mathematical Representation**: - 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. - This formula shows that the centripetal force depends on the mass of the object and the square of its speed, divided by the radius of the circle. 4. **Why Other Options Are Incorrect**: - **Option A**: "Centripetal force is an outward force that causes an object to move in a straight line." - This statement is incorrect because centripetal force is not an outward force; rather, it is directed inward towards the center of the circular path. The idea of an "outward force" is a common misconception; what people often refer to as an outward force is actually the inertia of the object trying to move in a straight line. - **Option C**: "Centripetal force increases as the radius of the circular path decreases." - This statement is misleading. While it is true that for a given mass and speed, a smaller radius would require a greater centripetal force (as seen in the formula \(F_c = \frac{mv^2}{r}\)), it does not mean that the centripetal force itself increases simply because the radius decreases. The centripetal force is dependent on the speed and mass of the object as well. If the speed remains constant, then yes, a smaller radius would require a larger centripetal force, but this statement lacks the necessary context. - **Option D**: "Centripetal force is only required when objects are in uniform circular motion." - This statement is incorrect because centripetal force is required for any type of circular motion, whether uniform (constant speed) or non-uniform (changing speed). In non-uniform circular motion, the object may also experience tangential acceleration, but centripetal force is still necessary to keep the object moving in a circular path. ### Common Pitfalls: - Confusing centripetal force with centrifugal force: Centrifugal force is not a real force; it is a perceived force that appears when observing motion in a rotating reference frame. - Misunderstanding the direction of centripetal force: Remember that it always points towards the center of the circular path, not outward. ### Revision Summary: - Centripetal force is directed towards the center of the circular path and acts perpendicular to the object's velocity. - It is essential for maintaining circular motion and is calculated using the formula \(F_c = \frac{mv^2}{r}\). - Centripetal force is not an outward force and is required for both uniform and non-uniform circular motion. - Be cautious of common misconceptions regarding the nature and direction of centripetal force.