Class 11 CH 8

GRAVITATION
CLASS: XI CHAPTER :8
The universe consists of galaxies,
stars, planets, comets etc. The force
which keeps them bound together is
called Gravitational force. Gravitation
is a natural phenomenon in which
material objects attract each other.
In 1687, Sir Isaac Newton

published universal law of
gravitation.
Newton’s 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.
If m1 and m2 are the masses of the particle and ‘r’ be the distance between their centers,
then the force of attraction ‘ F’ between them is given by
Where, G is the Universal

Gravitational Constant.
G= 6.67x10-11 Nm²kg-2
Characteristics of Gravitational Force:
▪ Gravitational force is independent of the medium.

▪ It is an attractive force.
▪ This force acts along the line joining the masses, hence it is a
central force.
▪ Gravitational force is a conservative force.

(ie, the work done by the gravitational force depends only on
the initial and final position, not on the path)
▪It obeys Newton’s 3rd law. The force exerted by the first
particle on the second is exactly equal and opposite to
the force exerted by the second particle on the first.
F12 = - F21
1. Two bodies of masses 10 kg and 6x10 24kg are placed

with their centers 6.4x106 m apart. Calculate the force of
attraction between the two masses. Also find the initial
acceleration of the two masses.( Assume that no other
forces act on them)
Ans:
6.4x106
10kg
6x10 24kg
F= Gm1 m2/ r²
= (6.67 x 10-11 x10 x 6x10 24 )/ (6.4x106 )²
= 97.7 N
For finding the acceleration,
F= ma
a= F/m
For Earth, a= 97.7/ 6x10 24 For small mass, a= 97.9/10
= 16.2x 10-24 = 9.7 m/s²
~0
(This is towards the small particle ) (This is towards Earth)
• Acceleration due to gravity of the Earth: ( g)
we know, F= Gm1m2/r²
Consider Earth,
Mass of Earth, M= 6x10 24kg
Radius of earth, R = 6.4x106 m
Consider a person of mass ‘m’ on the surface of earth,

The gravitational force acting on that person
F1= GMm/R²
• Here, the value of the term GM/R² is a constant = g
• = GM/ R²
• = (6.67 x 10-11 x 6x10 24 )/ (6.4x106 )²
• = 9.8 m/s²
The radius of the earth is more at the equator, so the value of ‘g’ slightly
increases while moving towards poles.
Variation of acceleration due to gravity of
Earth:
• Effect of height
• Effect of depth
• Effect of shape
• Gravitational Field
• It is an imaginary field due to the gravitational force.

Intensity of Gravitational field/Strength of Gravitational
field:
• Field is not measurable but gravitational field strength is

measurable.
• If we keep a body of mass ‘m’ in the gravitational field and F is
the force exerted by the field on that mass, then
Intensity of the field, I = F/m
If a mass m is placed close to the surface of Earth, the force on it
is mg.
ie I = F/m = mg/m = g
The intensity of the gravitational field near the surface of the

earth is equal to the acceleration due to gravity.
Gravitational Potential:
• The gravitational potential at a point in the gravitational

field of a body is defined as the amount of work done in
bringing a body of unit mass from infinity to that point.
Gravitational potential at a point situated at a distance r

from a body or particle of mass M is given by
• Gravitational Potential Energy
The work done in carrying a mass ‘m’ from infinity to a point at

distance r is called gravitational potential energy.
The gravitational potential energy of the system is given by
i.e., Gravitational potential energy = gravitational potential x

mass of the body.
It is a scalar quantity and measured in joule.
• ESCAPE VELOCITY
Satellite
A satellite is a body which is revolving continuously in an orbit around a
comparatively much larger body.
The orbit may be either circular or elliptical. A man-made object revolving in
an orbit around a planet is called an artificial satellite.
Artificial Satellites
EXERCISE:
8.7 Does the escape speed of a body from the earth depend on (a) the
mass of the body, (b) the location from where it is projected, (c) the
direction of projection, (d) the height of
the location from where the body is launched?
Solution:
• The escape speed is given by the expression
• The escape speed of a body from the Earth does not depend on the
mass of the body.
(b) The escape speed of a body from the Earth does not depend on
the location from where a body is projected.
(c) The escape speed does not depend on the direction of projection
of a body.
(d) The escape speed of a body depends upon the height of the
location from where the body is launched since the escape velocity
depends on the gravitational potential at the point from which it is
launched. This potential in turn depends on the height.
• At what height is the value of ‘g’ half that on the surface of
earth?
• The gravitational force between two bodies is 2N. When the

distance between the masses is halved, what is the force
between them?
8.15 A body weighs 63 N on the surface of the earth. What is the

gravitational force on it due to the earth at a height equal to half
the radius of the earth?
8.16 Assuming the earth to be a sphere of uniform mass density,

how much would a body weigh halfway down to the centre of the
earth if it weighed 250 N on the surface?
• Find the value of acceleration due to gravity at a height 100 km

above the surface. ( R = 6400km, g = 9.8m/s2

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GRAVITATION

In 1687, Sir Isaac Newton

Where, G is the Universal

▪ Gravitational force is independent of the medium.

▪ Gravitational force is a conservative force.

1. Two bodies of masses 10 kg and 6x10 24kg are placed

Consider a person of mass ‘m’ on the surface of earth,

• It is an imaginary field due to the gravitational force.

• Field is not measurable but gravitational field strength is

The intensity of the gravitational field near the surface of the

• The gravitational potential at a point in the gravitational

Gravitational potential at a point situated at a distance r

The work done in carrying a mass ‘m’ from infinity to a point at

The gravitational potential energy of the system is given by

i.e., Gravitational potential energy = gravitational potential x

• The gravitational force between two bodies is 2N. When the

8.15 A body weighs 63 N on the surface of the earth. What is the

8.16 Assuming the earth to be a sphere of uniform mass density,

• Find the value of acceleration due to gravity at a height 100 km

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