**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, ensuring that the satellite maintains its circular path. ### Why the Other Options are Incorrect: **Option A: A car accelerating in a straight line on a flat road** - This scenario does not involve circular motion. The car is moving in a straight line, and thus there is no centripetal force acting on it. Instead, the forces acting on the car are related to its acceleration (like friction and engine force), but they do not provide a centripetal force. **Option C: A ball thrown vertically upwards** - When a ball is thrown vertically, it moves up and then comes back down due to gravity. This motion is linear, not circular. The forces acting on the ball are gravitational force and the initial force from the throw, but again, there is no centripetal force involved since the path is not circular. **Option D: A cyclist racing downhill on a straight track** - Similar to Option A, the cyclist is moving in a straight line. The forces acting on the cyclist include gravity, friction, and possibly air resistance, but there is no centripetal force because the motion is not circular. ### Summary of Key Points: - **Centripetal Force** is necessary for circular motion and acts towards the center of the circular path. - **Correct Answer (B)**: A satellite in orbit experiences gravitational force as centripetal force, keeping it in a circular path. - **Incorrect Options**: A car accelerating straight (A), a ball thrown vertically (C), and a cyclist on a straight track (D) do not involve circular motion, hence no centripetal force. ### Revision Summary: - Centripetal force is essential for maintaining circular motion. - The gravitational force acts as centripetal force for satellites in orbit. - Straight-line motion scenarios do not involve centripetal force. - Always identify the nature of the motion (circular vs. linear) to determine the presence of centripetal force.