Prove that Newton’s Law of Gravitation follows Newton’s Third Law of Motion
Newton’s law of gravitation in vector form states that the gravitational forces acting between two masses are equal in magnitude and opposite in direction, forming an action-reaction pair.
Mathematical Representation
The vector form of Newton’s law of gravitation signifies that the gravitational forces acting between the two particles form action-reaction pair.
From the above figure, it can be seen that the two particles of masses are placed at a distance.
Thus, the forces are equal in magnitude but opposite in direction, satisfying Newton’s third law of motion.
Frequently Asked Questions (FAQs)
Q1. What is Newton’s law of gravitation?
A. 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 them.
Q2. Why is there a negative sign in the force equation?
A. The negative sign signifies that the gravitational force is attractive in nature.
Q3. Does Newton’s law of gravitation apply in a vacuum?
A. Yes, gravity acts in a vacuum since it does not require a medium to propagate.
Q4. What is the unit of gravitational force?
A. The SI unit of gravitational force is Newton (N).
Multiple Choice Questions (MCQs)
1. The force of gravitation between two bodies depends on:
a) The sum of their masses b) The difference of their masses c) The product of their masses d) The square of the sum of their masses Answer: (c) The product of their masses Explanation: Newton’s law states that gravitational force is directly proportional to the product of the two masses.
2. If the distance between two masses is doubled, the gravitational force will become:
a) Half b) One-fourth c) Double d) Four times Answer: (b) One-fourth Explanation: Since gravitational force follows an inverse square law, doubling the distance reduces the force by a factor of four.
3. Newton’s law of gravitation follows:
a) Newton’s first law b) Newton’s second law c) Newton’s third law d) None of these Answer: (c) Newton’s third law Explanation: The action-reaction pair in gravitational force satisfies Newton’s third law.
const questions = [
{
question: “Who formulated the law of universal gravitation?”,
options: [“Isaac Newton”, “Albert Einstein”, “Galileo Galilei”, “Johannes Kepler”],
correct: 0,
explanation: “Isaac Newton formulated the law of universal gravitation in the 17th century.”
},
{
question: “What is the equation for Newton’s law of gravitation?”,
options: [“F = G(m1m2)/r^2”, “F = ma”, “E = mc^2”, “F = kx”],
correct: 0,
explanation: “The correct equation is F = G(m1m2)/r^2, where G is the gravitational constant.”
},
{
question: “What happens to the gravitational force if the distance between two masses is doubled?”,
options: [“It becomes half”, “It becomes one-fourth”, “It doubles”, “It remains the same”],
correct: 1,
explanation: “Since gravitational force follows an inverse square law, doubling the distance reduces the force to one-fourth.”
},
{
question: “What does the negative sign in the vector form of gravitational force indicate?”,
options: [“Repulsion”, “Attraction”, “No effect”, “Acceleration”],
correct: 1,
explanation: “The negative sign signifies that the gravitational force is attractive.”
},
{
question: “What is the SI unit of gravitational force?”,
options: [“Newton”, “Joule”, “Kilogram”, “Meter”],
correct: 0,
explanation: “The SI unit of gravitational force is Newton (N).”
}
];function loadQuiz() {
const quizContainer = document.getElementById(“quiz”);
quizContainer.innerHTML = “”;
questions.forEach((q, index) => {
const questionBlock = document.createElement(“div”);
questionBlock.classList.add(“question-block”);
questionBlock.innerHTML = `
