Which one among the following statements is not correct?

The correct answer is Newton's law of gravitation follows from Newton's laws of motion..

Key Points

• Newton's law of gravitation is a standalone law that describes the attractive force between two masses and is not derived from Newton's laws of motion.
• Newton's laws of motion describe the relationship between the forces acting on a body and its motion, but they do not explain why bodies exert gravitational attraction.
• Newton's law of gravitation was formulated based on observational data and is independent of the three laws of motion.
• The gravitational force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them.
• Newton's laws of motion and the law of gravitation are foundational but distinct components of classical mechanics.

Additional Information

• Newton's Law of Gravitation:
  • States that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
  • Mathematically: F = G (m₁m₂)/r², where G is the gravitational constant.
• Newton's Laws of Motion:
  • First Law: A body remains at rest or in uniform motion unless acted upon by an external force (Law of Inertia).
  • Second Law: The rate of change of momentum of a body is directly proportional to the applied force (F = ma).
  • Third Law: For every action, there is an equal and opposite reaction.
• Gravitational Constant (G):
  • A fundamental constant of nature with a value of approximately 6.674 × 10⁻¹¹ N(m²/kg²).
  • It quantifies the strength of the gravitational force in Newton's law of gravitation.
• Gravitational Force vs. Weight:
  • Gravitational force is the mutual force of attraction between two masses.
  • Weight is the gravitational force exerted by the Earth on a body near its surface (Weight = mass × g).
• Gravitational Force at Earth's Center:
  • At the center of the Earth, the gravitational force due to the Earth's mass cancels out, resulting in zero acceleration due to gravity (g = 0).