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Gravitation Class 11 Notes Physics Chapter 7
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Page 1
Physics
Gravitation
The universe's constituents are galaxies, stars, planets, comets, asteroids, and
meteoroids. The force which keeps them bound together is called gravitational force.
Gravitation is a natural phenomenon by which material objects attract one another.
In 1687 A.D., English Physicist Sir Isaac Newton published Principia Mathematica,
which explains the inverse-square law of gravitation.
Newton’s law of gravitation:
? According to Newton's law of gravitation, “Everybody 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”. The directions of this force are along the line
joining the two bodies.
? The magnitude of gravitational force acting between two bodies of masses
1
m
and
2
m placed distance apart is
12
12 21 2
Gm m
FF
r
??
Where
12 21
FF ??
? It is a universal law.
? Universal Gravitational constant G is a scalar quantity. Its value is the same
throughout the universe and is independent of the nature and size of the bodies
as well as the nature of the medium between the bodies.
? The value of G in SI system is
11 2 2
6.67 10 Nm kg
??
? and in CGS system is
8 2 2
6.67 10 dynecm g
??
? .
Page 2
Physics
Gravitation
The universe's constituents are galaxies, stars, planets, comets, asteroids, and
meteoroids. The force which keeps them bound together is called gravitational force.
Gravitation is a natural phenomenon by which material objects attract one another.
In 1687 A.D., English Physicist Sir Isaac Newton published Principia Mathematica,
which explains the inverse-square law of gravitation.
Newton’s law of gravitation:
? According to Newton's law of gravitation, “Everybody 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”. The directions of this force are along the line
joining the two bodies.
? The magnitude of gravitational force acting between two bodies of masses
1
m
and
2
m placed distance apart is
12
12 21 2
Gm m
FF
r
??
Where
12 21
FF ??
? It is a universal law.
? Universal Gravitational constant G is a scalar quantity. Its value is the same
throughout the universe and is independent of the nature and size of the bodies
as well as the nature of the medium between the bodies.
? The value of G in SI system is
11 2 2
6.67 10 Nm kg
??
? and in CGS system is
8 2 2
6.67 10 dynecm g
??
? .
o The dimensional formula for G is
1 3 2
M L T
??
??
??
.
o The value of the universal gravitational constant G was determined
experimentally by English scientist Henry Cavendish in 1798.
Image: Newton’s law of gravitation
o Newton’s law of gravitation in vector form is,
12
2
ˆ .
Gm m
Fr
r
??
-ve sign shows that gravitational force is always attractive.
Characteristics of Gravitational Force:
The characteristics of gravitational force are as follows:
1. It is always attractive in nature
2. It obeys the inverse square law.
3. It is independent of the nature of the intervening medium.
4. It is independent of the presence or absence of other bodies.
5. It is independent of nature and the size of the bodies, till their masses remain
the same and the distance between their centres is fixed.
Principle of superposition of gravitation:
Page 3
Physics
Gravitation
The universe's constituents are galaxies, stars, planets, comets, asteroids, and
meteoroids. The force which keeps them bound together is called gravitational force.
Gravitation is a natural phenomenon by which material objects attract one another.
In 1687 A.D., English Physicist Sir Isaac Newton published Principia Mathematica,
which explains the inverse-square law of gravitation.
Newton’s law of gravitation:
? According to Newton's law of gravitation, “Everybody 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”. The directions of this force are along the line
joining the two bodies.
? The magnitude of gravitational force acting between two bodies of masses
1
m
and
2
m placed distance apart is
12
12 21 2
Gm m
FF
r
??
Where
12 21
FF ??
? It is a universal law.
? Universal Gravitational constant G is a scalar quantity. Its value is the same
throughout the universe and is independent of the nature and size of the bodies
as well as the nature of the medium between the bodies.
? The value of G in SI system is
11 2 2
6.67 10 Nm kg
??
? and in CGS system is
8 2 2
6.67 10 dynecm g
??
? .
o The dimensional formula for G is
1 3 2
M L T
??
??
??
.
o The value of the universal gravitational constant G was determined
experimentally by English scientist Henry Cavendish in 1798.
Image: Newton’s law of gravitation
o Newton’s law of gravitation in vector form is,
12
2
ˆ .
Gm m
Fr
r
??
-ve sign shows that gravitational force is always attractive.
Characteristics of Gravitational Force:
The characteristics of gravitational force are as follows:
1. It is always attractive in nature
2. It obeys the inverse square law.
3. It is independent of the nature of the intervening medium.
4. It is independent of the presence or absence of other bodies.
5. It is independent of nature and the size of the bodies, till their masses remain
the same and the distance between their centres is fixed.
Principle of superposition of gravitation:
It states that the resultant gravitational force F acting on a particle due to the number
of other particles is equal to the vector sum of the gravitational forces exerted by
individual particles on the given particle.
i.e.,
01 02 03 0 0
1
......
n
ni
i
F F F F F F
?
? ? ? ? ? ?
?
Where
01 02 03 0
, , ,...,
n
F F F F are the gravitational forces on a particle of mass
0
m due to
particles of masses
12
, ,....,
n
m m m respectively.
Gravity:
? It is defined as the force of attraction exerted by the earth towards its centre
on a body lying on or near the surface of the earth.
? It is merely a special case of gravitation and is also called earth's gravitational
pull.
? It is the measure of weight of the body.
? The weight of the body = mass(m) × acceleration due to gravity (g) = mg.
Acceleration due to Gravity:
? Acceleration produced in a body due to the force of gravity is called
acceleration due to gravity. It is denoted by symbol ‘g’ and mathematically it
is given by
2
e
GM
g
r
?
Where
e
M
the mass of the earth and r is is the distance of the body from the
centre of the earth
? If the body is on the surface of the earth i.e.
e
rR ? (radius of the earth), then
2
e
e
GM
g
R
?
Page 4
Physics
Gravitation
The universe's constituents are galaxies, stars, planets, comets, asteroids, and
meteoroids. The force which keeps them bound together is called gravitational force.
Gravitation is a natural phenomenon by which material objects attract one another.
In 1687 A.D., English Physicist Sir Isaac Newton published Principia Mathematica,
which explains the inverse-square law of gravitation.
Newton’s law of gravitation:
? According to Newton's law of gravitation, “Everybody 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”. The directions of this force are along the line
joining the two bodies.
? The magnitude of gravitational force acting between two bodies of masses
1
m
and
2
m placed distance apart is
12
12 21 2
Gm m
FF
r
??
Where
12 21
FF ??
? It is a universal law.
? Universal Gravitational constant G is a scalar quantity. Its value is the same
throughout the universe and is independent of the nature and size of the bodies
as well as the nature of the medium between the bodies.
? The value of G in SI system is
11 2 2
6.67 10 Nm kg
??
? and in CGS system is
8 2 2
6.67 10 dynecm g
??
? .
o The dimensional formula for G is
1 3 2
M L T
??
??
??
.
o The value of the universal gravitational constant G was determined
experimentally by English scientist Henry Cavendish in 1798.
Image: Newton’s law of gravitation
o Newton’s law of gravitation in vector form is,
12
2
ˆ .
Gm m
Fr
r
??
-ve sign shows that gravitational force is always attractive.
Characteristics of Gravitational Force:
The characteristics of gravitational force are as follows:
1. It is always attractive in nature
2. It obeys the inverse square law.
3. It is independent of the nature of the intervening medium.
4. It is independent of the presence or absence of other bodies.
5. It is independent of nature and the size of the bodies, till their masses remain
the same and the distance between their centres is fixed.
Principle of superposition of gravitation:
It states that the resultant gravitational force F acting on a particle due to the number
of other particles is equal to the vector sum of the gravitational forces exerted by
individual particles on the given particle.
i.e.,
01 02 03 0 0
1
......
n
ni
i
F F F F F F
?
? ? ? ? ? ?
?
Where
01 02 03 0
, , ,...,
n
F F F F are the gravitational forces on a particle of mass
0
m due to
particles of masses
12
, ,....,
n
m m m respectively.
Gravity:
? It is defined as the force of attraction exerted by the earth towards its centre
on a body lying on or near the surface of the earth.
? It is merely a special case of gravitation and is also called earth's gravitational
pull.
? It is the measure of weight of the body.
? The weight of the body = mass(m) × acceleration due to gravity (g) = mg.
Acceleration due to Gravity:
? Acceleration produced in a body due to the force of gravity is called
acceleration due to gravity. It is denoted by symbol ‘g’ and mathematically it
is given by
2
e
GM
g
r
?
Where
e
M
the mass of the earth and r is is the distance of the body from the
centre of the earth
? If the body is on the surface of the earth i.e.
e
rR ? (radius of the earth), then
2
e
e
GM
g
R
?
? It is also defined as the acceleration produced in the body while falling freely
under the effect of gravity alone.
? It is a vector quantity. Its SI unit is
2
ms
?
and its dimensional formula is
02
M LT
?
??
??
.
? The value of g on the surface of earth is taken to be
2
9.8ms
?
.
? The value of g varies with altitude, depth, shape, and the rotation of earth.
? The acceleration due to gravity (g) is related with gravitational constant (G)
by the relation
3
22
4
4
3
3
e
e
e
ee
GR
GM
g GR
RR
??
?? ? ? ?
Where
e
M is the mass of the earth,
e
R is the radius of the earth and ? in the
uniform density of the material of the earth.
? The acceleration value due to gravity is independent of the body's shape, size,
mass etc. of the body but depends upon mass and radius of the earth or planet
due to which there is a gravity pull.
F ma ?
2
GMm
ma
r
?
Then, cancelling m on both sides
2
GM
ag
r
??
Page 5
Physics
Gravitation
The universe's constituents are galaxies, stars, planets, comets, asteroids, and
meteoroids. The force which keeps them bound together is called gravitational force.
Gravitation is a natural phenomenon by which material objects attract one another.
In 1687 A.D., English Physicist Sir Isaac Newton published Principia Mathematica,
which explains the inverse-square law of gravitation.
Newton’s law of gravitation:
? According to Newton's law of gravitation, “Everybody 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”. The directions of this force are along the line
joining the two bodies.
? The magnitude of gravitational force acting between two bodies of masses
1
m
and
2
m placed distance apart is
12
12 21 2
Gm m
FF
r
??
Where
12 21
FF ??
? It is a universal law.
? Universal Gravitational constant G is a scalar quantity. Its value is the same
throughout the universe and is independent of the nature and size of the bodies
as well as the nature of the medium between the bodies.
? The value of G in SI system is
11 2 2
6.67 10 Nm kg
??
? and in CGS system is
8 2 2
6.67 10 dynecm g
??
? .
o The dimensional formula for G is
1 3 2
M L T
??
??
??
.
o The value of the universal gravitational constant G was determined
experimentally by English scientist Henry Cavendish in 1798.
Image: Newton’s law of gravitation
o Newton’s law of gravitation in vector form is,
12
2
ˆ .
Gm m
Fr
r
??
-ve sign shows that gravitational force is always attractive.
Characteristics of Gravitational Force:
The characteristics of gravitational force are as follows:
1. It is always attractive in nature
2. It obeys the inverse square law.
3. It is independent of the nature of the intervening medium.
4. It is independent of the presence or absence of other bodies.
5. It is independent of nature and the size of the bodies, till their masses remain
the same and the distance between their centres is fixed.
Principle of superposition of gravitation:
It states that the resultant gravitational force F acting on a particle due to the number
of other particles is equal to the vector sum of the gravitational forces exerted by
individual particles on the given particle.
i.e.,
01 02 03 0 0
1
......
n
ni
i
F F F F F F
?
? ? ? ? ? ?
?
Where
01 02 03 0
, , ,...,
n
F F F F are the gravitational forces on a particle of mass
0
m due to
particles of masses
12
, ,....,
n
m m m respectively.
Gravity:
? It is defined as the force of attraction exerted by the earth towards its centre
on a body lying on or near the surface of the earth.
? It is merely a special case of gravitation and is also called earth's gravitational
pull.
? It is the measure of weight of the body.
? The weight of the body = mass(m) × acceleration due to gravity (g) = mg.
Acceleration due to Gravity:
? Acceleration produced in a body due to the force of gravity is called
acceleration due to gravity. It is denoted by symbol ‘g’ and mathematically it
is given by
2
e
GM
g
r
?
Where
e
M
the mass of the earth and r is is the distance of the body from the
centre of the earth
? If the body is on the surface of the earth i.e.
e
rR ? (radius of the earth), then
2
e
e
GM
g
R
?
? It is also defined as the acceleration produced in the body while falling freely
under the effect of gravity alone.
? It is a vector quantity. Its SI unit is
2
ms
?
and its dimensional formula is
02
M LT
?
??
??
.
? The value of g on the surface of earth is taken to be
2
9.8ms
?
.
? The value of g varies with altitude, depth, shape, and the rotation of earth.
? The acceleration due to gravity (g) is related with gravitational constant (G)
by the relation
3
22
4
4
3
3
e
e
e
ee
GR
GM
g GR
RR
??
?? ? ? ?
Where
e
M is the mass of the earth,
e
R is the radius of the earth and ? in the
uniform density of the material of the earth.
? The acceleration value due to gravity is independent of the body's shape, size,
mass etc. of the body but depends upon mass and radius of the earth or planet
due to which there is a gravity pull.
F ma ?
2
GMm
ma
r
?
Then, cancelling m on both sides
2
GM
ag
r
??
Image: Acceleration due to gravity formula
Variation of Acceleration due to Gravity:
? Due to altitude (h): The acceleration due to gravity at height h above the
earth’s surface is given by
? ?
2
2
1
e
h
e
e
GM h
gg
R
Rh
?
??
? ? ?
??
?
??
2
e
e
GM
g
R
??
??
??
??
For
e
hR ??
2
1
h
e
h
gg
R
??
? ? ?
??
??
When we move above the earth’s surface, the acceleration value due to gravity
decreases.
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FAQs on Gravitation Class 11 Notes Physics Chapter 7
| 1. What is gravitation and how does it work? |  |
| 2. What is the difference between weight and mass? | |
Ans. Weight and mass are often used interchangeably, but they have different meanings. Mass refers to the amount of matter in an object and is measured in kilograms, while weight is the force exerted on an object due to gravity and is measured in newtons. Mass remains the same regardless of the location, while weight can vary depending on the strength of the gravitational field.
| 3. How does the value of gravitational acceleration change with height? | |
Ans. The value of gravitational acceleration, denoted by 'g', decreases as you move further away from the Earth's surface. This means that the force of gravity on an object decreases with increasing height. The exact rate at which 'g' changes depends on the distance from the center of the Earth and the mass of the Earth.
| 4. What is the significance of Newton's Universal Law of Gravitation? | |
Ans. Newton's Universal Law of Gravitation is a fundamental principle in physics that describes the force of gravity between two objects. It states that the force of gravity is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This law has been used to explain and predict the motion of celestial bodies and is crucial in understanding the mechanics of the universe.
| 5. Can the force of gravity be completely eliminated? | |
Ans. No, the force of gravity cannot be completely eliminated. Gravity is a fundamental force of nature and is always present. However, its effects can be weakened or canceled out by other forces. For example, astronauts in space experience a sensation of weightlessness because they are in freefall around the Earth, where the force of gravity and the force of their acceleration cancel each other out.
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