"The force of attraction between any two particles in the universe is called gravitation or gravitation force".
Newton's universal law of gravitation states that "Every particle in the universe attracts every other particle with of force which is directly proportional to the product of two masses and inversely proportional to the square of the distance between them ".
Do You Know?
 The value of G = 6.67 × 10^{11} N m^{2} kg^{2} or 6.67 × 10^{8} dyn cm^{2} g^{2}.
 The value of G is same throughout the universe and hence G is known as universal gravitational constant.
 Value of G was determined in laboratory by Sir Henry Cavendish.
 Since the value of G is very small, so the gravitational force is a very weak force.
 The gravitational force between a body on the earth is called gravity.
The Universal law of gravitation given by Newton has explained successfully several phenomena such as:
Interesting Fact:
Since the gravitational force of the planets like Mercury and Venus is very small, therefore, these planets do not have any satellite or moon.
Now you must be thinking that Pluto also has small mass then why it has Moons?
This is because Mercury and Venus are closer to the Sun, which has a stronger gravitational pull that has likely engulfed any potential moons for Mercury and Venus.
The formula applied for calculating gravitational force between light objects and heavy objects is the same, i.e.,
The formula for the force between Objects
Let us take three cases:
(i) When two bodies of mass 1 kg each are 1 meter apart.
Sol.
m_{1}= m_{2} = 1 kg, r = 1 m
Taking G = 6·67 × 10^{11} Nm^{2}/kg^{2}, we obtain the gravitational force of attraction,
which is extremely small. Hence, we conclude that though every pair of two objects exert gravitational pull on each other, yet they cannot move towards each other because this gravitational pull is too weak.
(ii) When a body of mass 1 kg is held on the surface of Earth.
Sol.
Here, m_{1} = 1 kg
m_{2} = mass of Earth = 6 × 10^{24} kg
r = distance of body from centre of Earth = radius of Earth = 6400 km = 6.4 × 10^{3}km = 6·4 × 10^{6} m
The gravitational force of attraction between the body and Earth,
It means that the Earth exerts a gravitational force of 9·8 N on a body of mass one kg. This force is much larger compared to the force when both bodies are lighter. That is why when a body is dropped from a height, it falls to the Earth.
(iii) When both bodies are heavy.
Sol.
Let us calculate the gravitational force of attraction between Earth and the Moon.
Mass of Earth, m_{1} = 6 × 10^{24} kg
Mass of Moon, m_{2} = 7.4 × 10^{22} kg
Distance between Earth and Moon, r = 3.84 × 10^{5} km = 3.84 × 10^{8} m
Gravitational constant, G = 6·67 × 10^{11} Nm^{2}/kg^{2}
The gravitational force between Earth and the Moon,
which is really large. It is this large gravitational force exerted by the Earth on the Moon, that makes the Moon revolve around the Earth.
Q. Find the gravitational force of attraction between two spheres each of mass 1000 kg. The distance between the centers of the spheres is 0.5 m.
Solution: Mass = m1 = m2 = 1000 kg
Distance between the centers = d = 0.5 m
Gravitational constant = G = 6.673 × 1011 Nm2kg2
Gravitational force = F = ?
F = Gm1m2/d^{2}
F = 6.673 × (10)^{11} × 1000 × 1000/(0.5)^{2}
= 6.673 * (10)11 * (10)6 /0.25
= 6.673 * (10)5 /0.25
= 26.692 * (10)5
= 2.67 × 104 N
Q. The gravitational force between two identical lead spheres kept at 1 m apart is 0.006673 N. Find their masses.
Solution: Gravitational force = F = 0.006673 N
Gravitational constant = G = 6.673 × 1011 Nm2kg2
Distance between the masses = d = 1m
Mass = m1 = m2 =?
F = Gm1m2/d^{2}
F = m^{2}/d^{2} (Let m1 = m2 = m)
m^{2} = F*d^{2}/G
m^{2} = 0.006673 * (1)^{3 }/ 6.673*(10)^{11}
Taking square root on both side
m = 10^{4 }= 10000 kg each
Therefore, mass of each lead sphere is 10000 kg.
80 videos352 docs97 tests

1. What is centripetal force? 
2. What is the Universal Law of Gravitation? 
3. What are the characteristics of gravitational force? 
4. Why is the Universal Law of Gravitation important? 
5. How does Newton's Universal Law of Gravitation explain the gravitational force between light objects and heavy objects? 
80 videos352 docs97 tests


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