IIT (NTSE/Olympiad)  

Gravitation

Gravitation

a) Every two objects in the universe attract each other. This force of attraction is called 'Gravitational force'.
b) The force of attraction between any two
material particles is directly proportional to the product of the masses ofthe particles and inversely proportional to the square of the distance between them. It acts along the line joining the two particles.

∴ F ∝ m1m2 and F ∝
F =
c) G is the constant of proportionality which is called 'Newton's gravitation constant.
G = 6.67 × 10-11Nm2/kg2
G = 6.67 × 10-8 dyne cm2/gm2
d) Dimensional formula of G is [ M-1 L3 T-2]
e) In vector form, the force exerted by point mass (2) on point mass (1) will be -

direction of is from 1 to 2.

similarly,
f) = -
but, || = ||
From above two expression we can conclude that the force exerted between two particles is equal in magnitude but opposite in direction.
g) Gravitational force is the weakest force in nature.
NOTE :
The ratio of gravitational to electrostatic force between two electrons is of the order.
Fg/Fe = 10-43.
h) The range of this force is maximum upto infinity.
i) It is due to very small value of G that we do not experience the gravitational force in our daily life. But masses of celestial bodies are so large that the magnitude of the force of attraction between them is appreciable. In the motion of planets and satellites, this force supplies the necessary centripetal force due to which earth revolves around the sun and moon around the earth.
j) If the density of the earth is assumed to be uniform and a particle moves inside the earth then the gravitational force decreases because the shell of the material lying outside the particle's radial position would not exert any force on the particle.


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