Foundation
Physics Foundation
Gravitation
Question
State Newton's law of gravitation. Obtain the relation between universal gravitational constant and gravitational acceleration on the surface of the earth.
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Solution
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According to Newton's Law of gravitational, every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them. [Fig. (1)]

F=Gm1m2r2             (where G is the universal gravitational constant)

Now, If m1 is earth's mass M and m2 is the mass of block m kept on the earth's surface. The distance between the center of the earth to the block is equal to the radius of the earth R.
∴ Force on the block, F=GMmR2
Where R is the radius of the earth. [Fig. (2)]

As we know that, acceleration due to gravity is the force by the earth on any block per unit mass of the block.
Acceleration due to gravity, =g=Fm=GMmR2×m
g=GmR2
This is the relation between universal gravitational constant and gravitational acceleration on the surface of the earth.