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?"
Universal Law of gravitation
Understanding the Universal Law of Gravitation
The question describes a fundamental principle in physics that governs the attractive force between any two objects in the universe. This principle is known as the Universal Law of Gravitation.
What is the Universal Law of Gravitation?
According to the Universal Law of Gravitation, every particle or object in the universe attracts every other particle or object with a force. This force has specific characteristics:
- It is directly proportional to the product of their masses. This means if you increase the mass of either object (or both), the gravitational force between them increases.
- It is inversely proportional to the square of the distance between their centers. This means if you increase the distance between the objects, the gravitational force between them decreases rapidly (specifically, by the square of the factor by which the distance increased).
Mathematically, the gravitational force (\(F\)) 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, which is a universal constant. Its value is approximately \(6.674 \times 10^{-11} \, \text{N} \cdot \text{m}^2 / \text{kg}^2\).
Analyzing the Options
Let's look at why the other options do not fit the description provided in the question:
- Kepler's Law: Kepler's laws describe the motion of planets around the Sun. They explain the paths, speeds, and periods of planetary orbits but do not state the general principle of attraction between any two objects based on their masses and distance.
- Newton's third Law of motion: This law states that for every action, there is an equal and opposite reaction. It deals with forces acting between interacting bodies but does not specifically describe the nature of the gravitational force related to mass and distance.
- Newton's first Law of motion: This law describes inertia, stating that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. It is about the state of motion rather than the calculation of forces like gravity.
Based on the description provided in the question, which explicitly mentions the proportionality to the product of masses and inverse proportionality to the square of the distance, the correct law is the Universal Law of Gravitation.
| Law | Description |
|---|---|
| Universal Law of Gravitation | Describes the attractive force between any two objects based on their masses and the distance between them. |
| Kepler's Laws | Describe planetary motion around the Sun. |
| Newton's first Law of motion | Law of inertia; describes the state of motion in the absence of force. |
| Newton's third Law of motion | Action-reaction principle; describes forces acting between interacting objects. |
Revision Table: Key Physics Laws
| Law Name | Core Concept | Relevance to Gravity Question |
|---|---|---|
| Universal Law of Gravitation | Force ∝ (Product of Masses) / (Distance)$^2$ | Directly matches the description. |
| Kepler's Laws | Planetary orbits | Describes orbits, not the fundamental force. |
| Newton's first Law of motion | Inertia | Describes motion, not the gravitational force calculation. |
| Newton's third Law of motion | Action-Reaction | Describes force pairs, not the nature of the gravitational force itself. |
Additional Information on Gravitational Force and Universal Law
The Universal Law of Gravitation is one of the most important laws in physics. It explains many phenomena, including:
- Why objects fall towards the Earth.
- The motion of the Moon around the Earth.
- The motion of planets around the Sun (which Kepler's laws describe as a consequence of this force).
- The tides in oceans.
The concept of the force being inversely proportional to the square of the distance is called an inverse-square law. Many fundamental forces in physics, like the electrostatic force, follow an inverse-square law.
It's important to remember that gravity is always an attractive force. Unlike electric forces which can be attractive or repulsive, gravitational force always pulls objects towards each other.
Important Questions from Universal law of gravitation
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-
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?
