In this section, you will get class 9 Physics Gravitation notes. Here, the topics like gravitation, Newton’s law of gravitation, acceleration due to gravity, free fall have been discussed. These notes are going to be very useful for you.
Table of Contents
Force of Gravitation
Force of gravitation is a force with which everybody in this universe attracts every other body towards itself. It is the force that is responsible for functioning of the solar system, formation of tides in seas, birth of black holes, presence of atmosphere on earth and perception of weight etc.
Newton’s Law of Gravitation
To measure the amount of force with which one body attracts every other body in this universe, Newton gave a law known famously as “Newton’s law of gravitation”.
According to this law, every body in this universe attracts every other body with a gravitational force, that is;
- directly proportional to the product of their masses, and,
- inversely proportional to the square of the distance separating them.
If two bodies of masses \(m_1\) and \(m_2\) are separated by a distance \(r\), and let \(f\) be the force of attraction between them. Then according to the Newton’s law;
\(F \propto m_1 m_2 , \tag{1} \)
\(\text{and }F \propto \frac{1}{r^2} \tag{2}\)
On combining (1) and (2), we get;
\[
F \propto \frac{m_1 m_2}{r^2}
\]
\[
\text{Or }F = G \frac{m_1 m_2}{r^2}
\]
Where (G) is a constant of proportionality and is called universal gravitational constant. It is called so, because its value remains same through out the universe.
Gravitation vs Gravity
Gravitation is the force of attraction between any two bodies of the universe, where as gravity is the force of attraction between Earth and any other body. It means when one among the two bodies is Earth, the force of gravitation is then called gravity.
Acceleration Due to Gravity
Whenever one body moves towards the other body due to the force of gravitation, its motion is accelerated. This acceleration possessed by the moving body is called acceleration due to gravity. It is denoted by \(g\) and its value on the surface of earth is \(9.8ms^2.\)
Expression for Acceleration Due to Gravity
Let’s consider a body of mass \(m\) near the surface of earth of mass \(M\) and radius \(R\). Now, according to the Newton’s law of gravitation, the force between the two bodies is given by;
\[
F = G \frac{m M}{R^2} \tag{1}
\]
Now, according to Newton’s second law of motion, the force acting on the body is given by
\[
F = m g \tag{2}
\]
On comparing (1) and (2), we can write;
\[m g = G \frac{m M}{R^2}\]
\[\text{Or } g = G \frac{M}{R^2}\]
This is the expression for the acceleration due to gravity. From this expression, we conclude that;
- acceleration due to gravity is independent of the mass of the falling body.
- it is directly proportional to the mass of the pulling body.
- it is inversely proportional to the square of the radius of the pulling body.
Variation of Acceleration Due to Gravity (g)
The value of acceleration due to gravity (g) is not constant unlike the value of G.
The value of g;
- decreases with depth or as we move into the earth.
- decreases with height.
- varies with the shape of earth. Its value is maximum at poles and minimum at equator.
- varies as we go from one planet to another planet.
Difference Between G & g
| G | g |
|---|---|
| It is known as the Universal gravitational constant | It is known as the acceleration due to gravity |
| Its value is constant through out the universe | Its value changes from place to place |
| Its value is \(\scriptsize 6.67 \times 10^{-11}Nm^2kg^{-2}\) | Its value is \(9.8ms^2\) |
| It is equal to the force that exists between the two bodies, each of unit mass and separated by a unit distance. | It is the ratio of force experienced by a body to its mass. |
Free Fall
Whenever an object moves under the effect of gravitational force alone, it is said to be in free fall.
For example, if a ball is dropped from a building, it falls just under the effect of the Earth’s gravitational force, and therefore it is said to be in free fall. Similarly, the satellites moving around Earth are also in free fall as the only force acting on them is the Earth’s gravitational force.
Kindly note that;
- during free fall, all the bodies move with the same acceleration \(g\).
- during free fall, all the bodies experience weightlessness.
FAQs
Why Earth has an atmosphere and moon does not?
Earth has an atmosphere as its gravitational pull is strong enough to hold the air around it, Whereas the gravitational pull of moon is very weak and it cannot hold the air around it. The thermal velocity of air particles on moon is large enough to easily overcome its gravitational pull, thus leaving it without an atmosphere.
Why do astronauts in spacecrafts experience weightlessness?
The astronauts in spacecrafts experience weightlessness as they along with their satellites are in free fall towards earth. As we know during free fall, weight experienced is zero, so they have an apparent weight equal to zero.
Why do we see high tides during full moon nights?
During full moon nights moon is very close to earth and therefore its gravitational pull on the water present on earth is very high. This in turn leads to the formation of high tides.
So, these were Class 9 Physics gravitation notes. Kindly comment whether you found them useful or not.
