**Correct Option: C. To maintain the object's circular path** ### Detailed Explanation: Centripetal force is a crucial concept in understanding circular motion. Let's break down its role and why option C is the correct answer. 1. **Understanding Circular Motion**: - When an object moves in a circular path, it is constantly changing direction. This change in direction means that the object is accelerating, even if its speed (the magnitude of its velocity) remains constant. This acceleration is directed towards the center of the circle. 2. **What is 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. It is not a separate force but rather the resultant of various forces acting on the object (like tension, gravity, friction, etc.) that keep it in circular motion. 3. **Why is Centripetal Force Necessary?**: - Without centripetal force, an object would not be able to maintain its circular path. Instead, it would move off in a straight line due to inertia (Newton's First Law of Motion). The centripetal force continuously pulls the object towards the center, allowing it to follow a curved trajectory. 4. **Mathematical Representation**: - The formula for centripetal force (\(F_c\)) is given by: \[ F_c = \frac{mv^2}{r} \] where: - \(m\) = mass of the object, - \(v\) = speed of the object, - \(r\) = radius of the circular path. - This equation shows that the centripetal force depends on the mass of the object, the square of its speed, and the radius of the circle. 5. **Example Calculation**: - Suppose a car of mass 1000 kg is moving at a speed of 20 m/s around a circular track with a radius of 50 m. The centripetal force required to keep the car on the track can be calculated as follows: \[ F_c = \frac{mv^2}{r} = \frac{1000 \, \text{kg} \times (20 \, \text{m/s})^2}{50 \, \text{m}} = \frac{1000 \times 400}{50} = 8000 \, \text{N} \] - This means a net inward force of 8000 N is required to keep the car moving in a circle. ### Why Other Options are Incorrect: - **Option A: To increase the speed of the object**: - This option is incorrect because centripetal force does not increase the speed of the object. In uniform circular motion, the speed remains constant; the force only changes the direction of the velocity vector, not its magnitude. - **Option B: To decrease the object's mass**: - This option is incorrect as centripetal force does not affect the mass of the object. The mass remains constant regardless of the motion. Centripetal force is related to the motion of the object, not its intrinsic properties. - **Option D: To convert kinetic energy into potential energy**: - This option is also incorrect. Centripetal force does not convert kinetic energy into potential energy. In circular motion, the energy types involved do not change in this manner. Kinetic energy remains constant in uniform circular motion, while potential energy changes only in the context of gravitational fields or other conservative forces, not due to centripetal force. ### Revision Summary: - Centripetal force is essential for maintaining an object's circular path by acting towards the center of the circle. - It is calculated using the formula \(F_c = \frac{mv^2}{r}\). - It does not increase speed, affect mass, or convert energy types. - Understanding centripetal force is key to mastering concepts of circular motion in physics.