Which of the following law states that, "The force between two objects is directly proportional to the product of their masses?"

Question

Prepp Team · Accepted Answer

Understanding Force and Mass in Physics

The question asks us to identify the physics law that describes the relationship between the force between two objects and the product of their masses. Let's examine the options provided to determine which law fits this description.

Analyzing the Options

Law of motion: This term is quite broad and usually refers to Newton's three laws of motion, which describe how objects move and interact under forces. While force is involved, these laws primarily relate force to acceleration, momentum, and inertia, not specifically the force *between* two objects based on their masses.
Law of change of momentum: This is related to Newton's second law of motion, stating that the rate of change of momentum of an object is directly proportional to the net force applied to it and is in the direction of the net force. Again, this focuses on momentum change and force applied to a single object or system, not the mutual force between two objects due to their masses.
Law of inertia: This is Newton's first law of motion. It states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. This law describes the property of objects to resist changes in their state of motion and doesn't directly state a relationship between force and the product of masses of interacting objects.
Law of gravitation: This law, specifically Newton's Law of Universal Gravitation, describes the attractive force that exists between any two objects with mass. It explicitly states how this force depends on the masses of the objects and the distance between them.

The Law of Gravitation Explained

Newton's Law of Universal Gravitation is precisely the law that describes the force of attraction between any two objects having mass. The law is stated as follows:

Every particle attracts every other particle in the universe 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.

Mathematically, the force of gravitation (\(F\)) between two objects with masses \(m_1\) and \(m_2\), separated by a distance \(r\), is given by the formula:

\[F = G \frac{m_1 m_2}{r^2}\]

Here, \(G\) is the gravitational constant. From this formula, we can clearly see that the force \(F\) is directly proportional to the product of the masses (\(m_1 m_2\)):

\[F \propto m_1 m_2\]

This directly matches the statement in the question: "The force between two objects is directly proportional to the product of their masses".

Therefore, the law that states this relationship is the law of gravitation.

Law	Key Concept	Relevance to Question
Law of motion (Newton's Laws)	Relates force to acceleration, momentum, inertia.	Doesn't specifically state force depends on product of masses of interacting objects.
Law of change of momentum	Relates force to rate of momentum change.	Focuses on force on an object, not mutual force based on masses.
Law of inertia	Objects resist change in motion state.	Describes resistance to force, not the force between masses.
Law of gravitation	Attractive force between objects with mass.	States force is directly proportional to the product of masses.

Conclusion on the Law Stating Force Proportional to Product of Masses

Based on the analysis of the options and the definition of the Law of Gravitation, it is clear that the statement "The force between two objects is directly proportional to the product of their masses" is a fundamental part of the Law of Gravitation.

Revision Table: Key Physics Laws

Law	Brief Description	Mathematical Relation (if applicable)
Newton's 1st Law (Inertia)	Object maintains state of motion unless acted upon by force.	N/A
Newton's 2nd Law	Force equals mass times acceleration; relates force to momentum change.	\(F = ma\) or \(F = \frac{\Delta p}{\Delta t}\)
Newton's 3rd Law	For every action, there is an equal and opposite reaction.	\(F_{AB} = -F_{BA}\)
Law of Gravitation	Attractive force between masses proportional to product of masses and inversely proportional to square of distance.	\(F = G \frac{m_1 m_2}{r^2}\)
Law of Conservation of Momentum	Total momentum of an isolated system remains constant.	\(\sum p_{initial} = \sum p_{final}\)

Additional Information on Law of Gravitation

The Law of Gravitation, proposed by Sir Isaac Newton, is a fundamental law in physics. It explains phenomena ranging from the fall of an apple to the orbits of planets around the sun. Here are some additional key points about the law:

It is a universal law, meaning it applies to any two objects with mass anywhere in the universe.
The force is always attractive, pulling the two objects towards each other.
The gravitational constant \(G\) is a very small value (\(G \approx 6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2\)), which is why gravitational forces are only significant when at least one of the objects has a very large mass (like a planet or star).
The inverse square relationship with distance (\(1/r^2\)) means that if the distance between the objects doubles, the gravitational force becomes four times weaker.
This law was a monumental achievement, unifying terrestrial mechanics (like falling objects) with celestial mechanics (like planetary motion).