Universal law of Gravitation
The universal law of gravitation was given by Newton. So, it is also known as Newton’s law of gravitation. According to universal law of gravitation:- Every body in the universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The force is along the line joining the centres of two objects.
Let two objects A and B of masses M and m lie at a distance d from each other. Let the force of attraction between two objects be F. According to the universal law of gravitation, the force between two objects is directly proportional to the product of their masses. That is,
F ∝ M × m…………………………………………………(1)
And the force between two objects is inversely proportional to the square of the distance between them, that is,
F ∝ 1/d2…………………………………………………………(2)
From equation 1 and 2, we get
F ∝ M × m/d2
F = G M × m/d2
where G is the constant of proportionality and is called the universal gravitation constant.
F × d2 = G M × m
G = F d2/M × m
The SI unit of G is N m2 kg-2.
The value of G was found out by Henry Cavendish (1731-1810) by using a sensitive balance. The accepted value of G is 6.673 × 10-11 N m2 kg-2.
Example:- The mass of the earth is 6 × 1024 kg and that of the moon is 7.4 × 1022 kg. If the distance between the earth and the moon is 3.84 × 105 km, calculate the force exerted by the earth on the moon. G = 6.7 × 10-11 N m2 kg-2.
Sol:- The mass of the earth (M) = 6 × 1024 kg
The mass of the moon (m) = 7.4 × 1022 kg
The distance between the earth and the moon (d) = 3.84 × 105km
= 3.84 × 105 × 1000 m
= 3.84 × 108 m
G = 6.7 × 10-11 N m2 kg-2
F = G M × m/d2
F = 6.7 × 10-11 × 6 × 1024 × 7.4 × 1022/ (3.84 × 108)2
F = 2.01 × 1020 N
Thus, the force exerted by the earth on the moon is 2.01 × 1020N.
