The acceleration of a body moving in a circle of radius R with uniform speed v is v²/R directed towards the centre. Then according to which law, the force fc providing this acceleration is f_c = mv²/ R

The correct answer is Second law of motion.

Key Points

• The Second Law of Motion states that the force acting on an object is equal to the mass of the object multiplied by its acceleration, expressed as F = ma.
• In the case of circular motion, the centripetal force (Fc) required to keep the body moving in a circle is given by Fc = mv²/R, where m is mass, v is velocity, and R is radius.
• The acceleration experienced in circular motion is centripetal acceleration, directed towards the center, and its magnitude is v²/R.
• This law forms the basis for understanding the relationship between force, mass, and acceleration in both linear and circular motion scenarios.
• Newton's Second Law is universally applicable and provides the mathematical foundation for analyzing motion and dynamics in physics.

Additional Information

• Circular Motion Terminology:
  • Centripetal Force: The inward force required to keep an object moving in a circular path.
  • Centripetal Acceleration: Acceleration directed towards the center of the circle, calculated as v²/R.
  • Uniform Circular Motion: Motion of an object traveling at a constant speed along a circular path.
• Newton's Laws of Motion:
  • First Law: A body remains at rest or in uniform motion unless acted upon by an external force.
  • Second Law: Force is directly proportional to the rate of change of momentum (F = ma).
  • Third Law: For every action, there is an equal and opposite reaction.
• Applications of Centripetal Force:
  • Satellite motion in orbit around Earth.
  • Vehicles negotiating curved paths on roads.
  • Amusement park rides such as roller coasters.
• Historical Context:
  • Newton formulated the Second Law of Motion as part of his groundbreaking work in "Philosophiæ Naturalis Principia Mathematica" (1687).
  • It revolutionized the understanding of motion and dynamics, forming the core of classical mechanics.