Comprehensive Question 1: State and explain the law of universal gravitation. Also show that the law obeys Newton’s third law of motion.
Answer
Statement of the Law of Universal Gravitation
Every body in the universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Explanation
Consider two bodies of masses m1 and m2 separated by distance r as shown in the figure.
According to Newton’s law of universal gravitation;
and
Combining
G is the constant of proportionality and the experimentally determined value is 6.67 × 10-11 N m2 kg-2.
We note the gravitational force is an inverse square force. This means it increases or decreases very rapidly with decrease or increase in the distance between the masses.
Secondly, G is independent of the medium between the two masses. It does not change with a change in the medium between the two bodies.
Law of universal gravitation obeys Newton’s Third Law of Motion
The force acting on mass m1 due to mass m2 is F21 and the force acting on mass m2 due to mass m1 is F12. We see both these forces are equal in magnitude and opposite in direction. This is in agreement with the Third Law of Motion, i-e, every force has an equal and opposite reaction. Therefore, Newton’s law of universal gravitation obeys his third law of motion.