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)
Understanding Gravitational Force Between Particles
The question asks for the formula that describes the force of attraction between two particles with given masses and separation. This force is known as the gravitational force, as described by Newton's Law of Universal Gravitation.
Newton's Law of Universal Gravitation states that every particle attracts every other particle in the universe with a force that is:
- Directly proportional to the product of their masses ($m_1$ and $m_2$).
- Inversely proportional to the square of the distance ($r$) between their centers.
Mathematically, this law is expressed as:
Where:
- \(F\) is the force of attraction between the two particles.
- \(G\) is the universal gravitational constant, a fundamental constant in physics.
- \(m_1\) and \(m_2\) are the masses of the two particles.
- \(r\) is the distance between the centers of the two particles.
Analyzing the Given Options for Gravitational Force
Let's examine each option based on Newton's Law of Universal Gravitation formula:
- Option 1: \(G\frac{m_1m_2}{r}\) - This formula shows the force is inversely proportional to the distance \(r\), not the square of the distance \(r^2\). This is incorrect.
- Option 2: \(G\frac{m_1m_2}{r^3}\) - This formula shows the force is inversely proportional to the cube of the distance \(r^3\). This is incorrect.
- Option 3: \(G\frac{m_1m_2}{r^2}\) - This formula matches the expression from Newton's Law of Universal Gravitation, where the force is inversely proportional to the square of the distance \(r^2\). This is the correct formula for the force of attraction.
- Option 4:
G.m 1.m 2.r 2
- This formula shows the force is directly proportional to the square of the distance \(r^2\), not inversely proportional. This is incorrect.
Therefore, the formula for the force of attraction between two particles with masses \(m_1\) and \(m_2\) separated by a distance \(r\), with \(G\) being the universal constant, is \(F = G\frac{m_1m_2}{r^2}\).
Revision Table: Gravitational Force Components
| Component | Description | Influence on Force (F) |
|---|---|---|
| Mass \(m_1\) | Mass of the first particle | Directly proportional ($F \propto m_1$) |
| Mass \(m_2\) | Mass of the second particle | Directly proportional ($F \propto m_2$) |
| Distance \(r\) | Distance between particle centers | Inversely proportional to square ($F \propto 1/r^2$) |
| Universal Constant \(G\) | Gravitational Constant | Proportional constant relating quantities |
Additional Information on Universal Gravitation
The universal gravitational constant \(G\) is a crucial value in this formula. It quantifies the strength of the gravitational force. Its value is approximately $6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2$. The 'universal' aspect of \(G\) means it is considered constant throughout the universe.
The inverse square relationship with distance ($1/r^2$) is a fundamental characteristic not just of gravity, but also of other forces like electrostatic force. This means that if the distance between the particles is doubled, the gravitational force becomes four times weaker ($1/(2r)^2 = 1/(4r^2)$).
Important Questions from Universal law of gravitation
Which of the following is NOT correct ?
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.
Which of the following is NOT correct ?
- Which phenomenon, successfully explained by the universal law of gravitation, relies on the combined and differential gravitational attraction exerted by both the moon and the sun on the earth?
- The law of gravitation helped to prove that:
