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Question
State the universal law of gravitation and derive its mathematical expression.
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Solution
This law states that every particle of matter in this universe attracts every other particle with a force. This force is directly proportional to the product of their masses and inversely proportional to the square of the distance between the centers of these masses. The direction of the force acts along the line joining the masses.
gravitational force between two masses
The force between the masses is always attractive and it does not depend on the medium where they are placed.
Let, m1 and m2 be the masses of two bodies A and B placed r metre apart in space.
Force F ∝ m1 × m2
F ∝ 1/r2
On combining the above two expressions
F ∝ `("m"_1xx"m"_2)/"r"^2`
F = `("Gm"_1"m"_2)/r^2`
Where G is the universal gravitational constant.
Its value in SI unit is 6.674 × 10-11 Nm2 kg-2.
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