The force of attraction between two objects of masses 'M' and 'm' which lie at a distance 'd' from each other is directly proportional to the-
Product of the masses of objects M × m
Understanding Gravitational Force and Mass
The question asks about the force of attraction between two objects based on their masses and the distance between them. This concept is described by Newton's Law of Universal Gravitation.
Newton's Law of Universal Gravitation states that every particle of matter 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, the gravitational force (\(F\)) between two objects with masses \(M\) and \(m\), separated by a distance \(d\), is given by the formula:
$$F = G \frac{Mm}{d^2}$$
Where:
- \(F\) is the force of gravitational attraction between the two objects.
- \(G\) is the gravitational constant, a universal constant.
- \(M\) is the mass of the first object.
- \(m\) is the mass of the second object.
- \(d\) is the distance between the centers of the two objects.
Proportionality of Gravitational Force
From the formula \(F = G \frac{Mm}{d^2}\), we can see how the force \(F\) depends on the masses \(M\) and \(m\), and the distance \(d\).
The formula shows that:
- The force \(F\) is directly proportional to the product of the masses \(M \times m\). This means if the product of the masses increases, the force of attraction increases proportionally, assuming the distance \(d\) remains constant.
- The force \(F\) is inversely proportional to the square of the distance \(d^2\). This means if the distance \(d\) increases, the force of attraction decreases rapidly (by the square of the distance), assuming the masses \(M\) and \(m\) remain constant.
- The gravitational constant \(G\) determines the strength of the gravitational force and is the same everywhere in the universe.
The question specifically asks what the force of attraction is directly proportional to, concerning the masses.
Looking at the formula \(F \propto Mm\), we can clearly see the direct relationship between the force \(F\) and the product of the masses \(Mm\).
Analyzing the Options based on Gravitational Force
Let's examine the given options in the context of Newton's Law of Universal Gravitation:
| Option | Description | Relation to Gravitational Force \(F\) | Is it directly proportional? |
|---|---|---|---|
| 1 | Sum of the masses \(M + m\) | Newton's law does not state this proportionality. | No |
| 2 | Product of the masses \(M \times m\) | According to Newton's law, \(F \propto Mm\). | Yes |
| 3 | Difference between masses \(M – m\) | Newton's law does not state this proportionality. | No |
| 4 | Sum of the squares of masses \(M² + m²\) | Newton's law does not state this proportionality. | No |
Based on the analysis of Newton's Law, the force of attraction between two objects is directly proportional to the product of their masses.
Conclusion on Gravitational Force and Mass Proportionality
The force of attraction between two objects with masses \(M\) and \(m\) at a distance \(d\) is given by \(F = G \frac{Mm}{d^2}\). This equation shows that the force \(F\) is directly proportional to the product of the masses \(M \times m\).
Therefore, the force of attraction is directly proportional to the product of the masses of the objects.
Revision Table: Key Concepts of Gravitational Force
| Concept | Description |
|---|---|
| Newton's Law of Universal Gravitation | Describes the force of attraction between any two objects with mass. |
| Gravitational Force (\(F\)) | The attractive force between two masses. |
| Masses (\(M, m\)) | The amount of matter in the objects. Force is directly proportional to their product. |
| Distance (\(d\)) | The separation between the centers of the objects. Force is inversely proportional to the square of the distance. |
| Gravitational Constant (\(G\)) | A fundamental constant determining the strength of gravity. |
| Formula | \(F = G \frac{Mm}{d^2}\) |
Additional Information on Universal Gravitation
Newton's Law of Universal Gravitation is a fundamental law in physics. It explains why planets orbit the sun, why objects fall to the Earth, and the tides on Earth.
- Gravity is always an attractive force, pulling objects towards each other.
- The force of gravity acts along the line connecting the centers of the two objects.
- Even small objects exert gravitational forces on each other, but these forces are usually negligible compared to the gravitational force exerted by large objects like planets or stars because the mass is much smaller.
- The inverse square relationship with distance means gravity weakens very quickly as objects move farther apart. Doubling the distance reduces the force to one-fourth, tripling it reduces the force to one-ninth, and so on.
Important Questions from Universal law of gravitation
Which of the following laws says that "Every object in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them?"
The force of attraction (F) between two particles having masses m 1and m 2is given by _______. (If r is the distance between them and G is a universal constant)
Three point masses each of mass m are placed at the three corners of an equilateral triangle of side x. Find the resultant force acting on any one particle at the corner.
Imagine a light planet is revolving around a star in a circular orbit of radius R with the period of revolution T . If the gravitational force of attraction between the two is proportional to R(-5/2) then
The force of attraction between two particles of masses m1 and m2 separated by distance d is given by:
F = Gm1m2/d2. What is the value of G?
