**Correct Option: B. It is always directed toward the center of the circular path.** ### Detailed Explanation: Centripetal force is a crucial concept in physics, particularly when discussing the motion of objects in circular paths. Let's break down the definition and implications of centripetal force step by step. 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. According to Newton's second law of motion, an acceleration requires a net force acting on the object. 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. This force is responsible for keeping the object in its circular trajectory. Without this force, the object would move off in a straight line due to inertia, as described by Newton's first law of motion. 3. **Direction of Centripetal Force**: - The defining characteristic of centripetal force is its direction. It always points towards the center of the circular path. This inward direction is essential because it continuously changes the direction of the object's velocity vector, allowing it to maintain circular motion. 4. **Mathematical Representation**: - The magnitude of centripetal force (\(F_c\)) can be calculated using the formula: \[ F_c = \frac{mv^2}{r} \] 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, the square of its speed, and the radius of the circle. 5. **Why Other Options are Incorrect**: - **Option A: It is the force that causes the object to move in a straight line.** - This statement is incorrect because centripetal force does not cause straight-line motion; rather, it prevents straight-line motion by continuously pulling the object towards the center of the circle. If there were no centripetal force, the object would indeed move in a straight line due to inertia. - **Option C: It acts in the opposite direction to the object's velocity.** - This option is misleading. While the centripetal force is directed towards the center of the circle, the object's velocity is tangential to the circular path. Therefore, centripetal force does not act opposite to the velocity; instead, it acts perpendicular to the velocity vector, changing the direction of the velocity without changing its magnitude. - **Option D: It increases as the speed of the object decreases.** - This statement is incorrect because, according to the centripetal force formula, if the speed (\(v\)) of the object decreases, the centripetal force also decreases, assuming mass and radius remain constant. Thus, centripetal force is directly proportional to the square of the speed. ### Summary: - Centripetal force is essential for maintaining circular motion, always directed towards the center of the circular path. - It prevents objects from moving in a straight line due to inertia. - The force is calculated using the formula \(F_c = \frac{mv^2}{r}\), showing its dependence on mass, speed, and radius. - Understanding the direction and nature of centripetal force is crucial for solving problems related to circular motion. ### Revision Summary: - Centripetal force is directed towards the center of the circular path. - It is necessary for keeping an object in circular motion. - The formula for centripetal force is \(F_c = \frac{mv^2}{r}\). - It does not act opposite to velocity and does not cause straight-line motion.