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2.5 GRAVITATION
In previous classes we have learnt about the motion of objects for which force is the cause.
We have learnt that a force is needed to change a speed or the direction of motion of an object.
We always observe that an object dropped from a height falls towards the earth. We know
that all the planets go around the sun. The moon goes around the earth. In all these cases, there
must be some force acting on the objects, planets, and on the moon.
Sir Isaac Newton could grasp that “The same force” is responsible for all of these. This
force is called the “gravitational force”.
Gravitation or gravity is a natural phenomenon, by which physical bodies attract one
another with a force, which is directly proportional to their masses. Gravity is not a property of the
earth alone. In fact every object in the universe, whether small or large, exerts a force on every
other object. This force is known as the gravitational force.
Solar System
SOLAR SYSTEM
Note :
1)
Gravitational force is one of the four basic forces of nature.
2)
Among the basic forces of nature, the gravitational force is the weakest.
3)
Gravitational force between two bodies is mutual. It acts along the line joining the two
bodies.
4)
The gravitational force between two bodies constitutes an action – reaction pair of forces.
5)
Galileo showed that gravitation accelerates all objects at the same rate.
This was a major departure from Aristotle’s belief that heavier objects accelerate
faster and lighter objects accelerate slower. Galileo correctly postulated that “air resistance”
as reason that lighter objects may fall more slowly in an atmosphere.
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Newton’s law of gravitation : It states that, every body in this 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 their centers.
Consider two bodies of masses m1 and m2, separated by a distance d.
According to the Newton’s law of gravitation, the force of attraction between the two
bodies, is
F ∝ m1m2
F∝ 1
d2
F ∝ m1m2
d2
mm
F = G 12 2
d
Where the constant of proportionality ‘G’ is known as universal constant of gravitation.
Definition of G : Universal constant of gravitation is numerically equal to the force of
attraction between two unit masses, placed at unit distance apart.
 newton − metre 2 
 or (Nm2 kg-2).
SI unit of G : The SI unit of G is 
2
 Ki log ram

1)
2)
3)
Note :
The value of G does not depend upon nature and size of the bodies.
It does not depend upon the nature of the medium between the two bodies.
Owing to the extremely small value of G, the gravitational force between even two big
rocks is very small.
Activity : We know that, there exists a force of attraction between any two objects.
Compute the value of this force of attraction between ‘you’ and ‘your friend’ sitting closely.
Explain why you do not feel this force.
Relation between g and G
Consider a body of mass m be placed on the surface of the earth .Let M be the mass of the
earth and R its radius.
From Newton’s law of gravitation force between them is given by,
GMm
F =
-- (1)
R2
The weight of the body is given by
F = W = mg -- (2)
From equation (1) and equation (2)
GMm
= mg
R2
GM
g=
R2
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Variation of acceleration due to gravity (g) with altitude (height):
The acceleration due to gravity g' at a height ‘h’ above the surface of the earth of radius R is
 2h 
given by, g ' = g 1 − 
R

Where, g is the acceleration due to gravity on the surface of the earth. This expression show
that acceleration due to gravity decreases with increase in altitude.
Variation of acceleration due to gravity (g) with depth:
The acceleration due to gravity g’ at a depth below the surface of the earth of radius R is
given by
h

g ' = g 1 − 
 R
Where, g is the acceleration due to gravity on the surface of the earth.
This expression shows that the acceleration due to gravity decreases with increase in depth .
Variation of acceleration due to gravity (g) with latitude:
The acceleration due to gravity g' at latitude θ on the surface
of the earth of radius R
and angular velocity ω is given by.
 ω2R

g ' = g 1 −
cos 2 θ 
g


Where, g is the acceleration due to gravity on the surface of the earth.
This expression shows that, acceleration due to gravity decreases due to rotation of the earth
Case (i): At the equator θ=0o and cosθ = cos0o =1
 ω 2R 

g ' = g 1 −
g 

Case (ii): At poles θ = 90o and cos θ = Cos90o=0
g’ = g
Thus acceleration due to gravity is least at the equator and maximum at the poles.
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Questions :
What is gravitation ?
Is gravitation is same for heavier and lighter objects ?
State Newton’s law of gravitation.
Mention the relation between g and G.
Write SI unit of gravitational constant ‘G’.
How does gravity ‘g’ varies with a altitude ?
How does gravity ‘g’ varies with a depth ?
What is the value of ‘g’ at the poles ?
What is the value of ‘g’ at the equator ?
What happens to the gravity at the “Centre of the earth” ?
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Answers
2.5 Gravitation
1) Gravitation is a natural phenomenon by which physical bodies attract one another with a force
which is directly proportional to their masses.
2) Yes. it is same for heavier and lighter objects .
3) It state that everybody in this 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 there centers .
4) g = GM.
R2
2
5) Nm Kg-2
6) Acceleration due to gravity ‘g’ decreases with increase in altitude above the surface of the
earth.
7) Acceleration due to gravity ‘g’ decreases with increase in depth below the surface of the earth.
8) The value of ‘g’ is maximum at the poles.
9) The value of ‘g’ is least at the equator.
10) It becomes zero at the centre of the earth.
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