**Correct Option: B. A satellite orbiting Earth in a circular path.** ### Detailed Explanation: **Understanding Centripetal Force:** Centripetal force is the force that keeps an object moving in a circular path. It acts towards the center of the circle around which the object is moving. This force is necessary because, without it, the object would move in a straight line due to inertia (Newton's first law of motion). **Why Option B is Correct:** In the case of a satellite orbiting Earth, the satellite is moving in a circular path around the planet. The gravitational force between the Earth and the satellite acts as the centripetal force that keeps the satellite in orbit. 1. **Gravitational Force as Centripetal Force:** - The gravitational force can be calculated using Newton's law of universal gravitation: \[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \] where \( F \) is the gravitational force, \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the Earth and the satellite, and \( r \) is the distance from the center of the Earth to the satellite. - This gravitational force provides the necessary centripetal force to keep the satellite in its circular orbit. 2. **Centripetal Acceleration:** - The satellite experiences centripetal acceleration, which can be expressed as: \[ a_c = \frac{v^2}{r} \] where \( v \) is the orbital speed of the satellite and \( r \) is the radius of the orbit. - The gravitational force acting on the satellite is equal to the required centripetal force, thus maintaining its circular motion. ### Why the Other Options are Incorrect: **Option A: A car driving straight along a flat road at a constant speed.** - This scenario does not involve any circular motion. The car is moving in a straight line, and while it may be traveling at a constant speed, there is no centripetal force acting on it. Centripetal force is only relevant when an object is changing direction, which is not the case here. **Option C: A ball rolling down a hill accelerating due to gravity.** - In this scenario, the ball is moving down a slope under the influence of gravity. While gravity is acting on the ball, it is not providing a centripetal force because the ball is not moving in a circular path. Instead, it is accelerating linearly down the hill. **Option D: A person jumping off a diving board into a pool.** - When a person jumps off a diving board, they are in free fall until they hit the water. This motion is not circular; therefore, there is no centripetal force involved. The forces acting on the person are gravity and air resistance, but these do not create a circular motion. ### Summary of Key Points: - **Centripetal Force** is necessary for circular motion and acts towards the center of the circular path. - **Correct Scenario (B)**: A satellite in orbit experiences gravitational force as centripetal force, keeping it in a circular path. - **Incorrect Scenarios**: Options A, C, and D do not involve circular motion, hence do not illustrate centripetal force. - **Key Formula**: Gravitational force provides the centripetal force necessary for circular motion, and centripetal acceleration can be calculated using \( a_c = \frac{v^2}{r} \). This understanding of centripetal force is crucial for analyzing any situation involving circular motion in physics.