Chapter 10
GRAVITATION
In Chapters 8 and 9, we have learnt about Let us try to understand the motion of
the motion of objects and force as the cause the moon by recalling activity 8.11.
of motion. We have learnt that a force is
needed to change the speed or the direction Activity _____________ 10.1
of motion of an object. We always observe that
• Take a piece of thread.
an object dropped from a height falls towards • Tie a small stone at one end. Hold the
the earth. We know that all the planets go other end of the thread and whirl it
around the Sun. The moon goes around the round, as shown in Fig. 10.1.
earth. In all these cases, there must be some • Note the motion of the stone.
force acting on the objects, the planets and • Release the thread.
on the moon. Isaac Newton could grasp that • Again, note the direction of motion of
the same force is responsible for all these. the stone.
This force is called the gravitational force.
In this chapter we shall learn about
gravitation and the universal law of
gravitation. We shall discuss the motion of
objects under the influence of gravitational
force on the earth. We shall study how the
weight of a body varies from place to place.
We shall also discuss the conditions for
objects to float in liquids.
10.1 Gravitation
We know that the moon goes around the
earth. An object when thrown upwards,
reaches a certain height and then falls
downwards. It is said that when Newton was
sitting under a tree, an apple fell on him. The Fig. 10.1: A stone describing a circular path with a
velocity of constant magnitude.
fall of the apple made Newton start thinking.
He thought that: if the earth can attract an
apple, can it not attract the moon? Is the force Before the thread is released, the stone
the same in both cases? He conjectured that moves in a circular path with a certain speed
the same type of force is responsible in both and changes direction at every point. The
the cases. He argued that at each point of its change in direction involves change in velocity
orbit, the moon falls towards the earth, or acceleration. The force that causes this
instead of going off in a straight line. So, it acceleration and keeps the body moving along
must be attracted by the earth. But we do the circular path is acting towards the centre.
not really see the moon falling towards the This force is called the centripetal (meaning
earth. ‘centre-seeking’) force. In the absence of this
2020-21
, force, the stone flies off along a straight line. 10.1.1 UNIVERSAL LAW OF GRAVITATION
This straight line will be a tangent to the
circular path. Every object in the universe attracts every
other object with a force which is proportional
to the product of their masses and inversely
Tangent to a circle
proportional to the square of the distance
between them. The force is along the line
joining the centres of two objects.
More to know
A straight line that meets the circle
at one and only one point is called a Mm
F = G 2
tangent to the circle. Straight line d
ABC is a tangent to the circle at
point B.
Fig. 10.2: The gravitational force between two
uniform objects is directed along the line
The motion of the moon around the earth joining their centres.
is due to the centripetal force. The centripetal
force is provided by the force of attraction of Let two objects A and B of masses M and
the earth. If there were no such force, the m lie at a distance d from each other as shown
moon would pursue a uniform straight line in Fig. 10.2. Let the force of attraction between
motion. two objects be F. According to the universal
It is seen that a falling apple is attracted law of gravitation, the force between two
towards the earth. Does the apple attract the objects is directly proportional to the product
earth? If so, we do not see the earth moving of their masses. That is,
towards an apple. Why? F∝M × m (10.1)
According to the third law of motion, the And the force between two objects is inversely
apple does attract the earth. But according proportional to the square of the distance
to the second law of motion, for a given force, between them, that is,
acceleration is inversely proportional to the
mass of an object [Eq. (9.4)]. The mass of an 1
apple is negligibly small compared to that of F∝ (10.2)
d2
the earth. So, we do not see the earth moving
towards the apple. Extend the same argument Combining Eqs. (10.1) and (10.2), we get
for why the earth does not move towards the
moon. M ×m
In our solar system, all the planets go F ∝ (10.3)
d2
around the Sun. By arguing the same way,
we can say that there exists a force between M×m
the Sun and the planets. From the above facts or, F = G 2 (10.4)
d
Newton concluded that not only does the
earth attract an apple and the moon, but all where G is the constant of proportionality and
objects in the universe attract each other. This is called the universal gravitation constant.
force of attraction between objects is called By multiplying crosswise, Eq. (10.4) gives
the gravitational force. F×d2=GM×m
132 SCIENCE
2020-21
GRAVITATION
In Chapters 8 and 9, we have learnt about Let us try to understand the motion of
the motion of objects and force as the cause the moon by recalling activity 8.11.
of motion. We have learnt that a force is
needed to change the speed or the direction Activity _____________ 10.1
of motion of an object. We always observe that
• Take a piece of thread.
an object dropped from a height falls towards • Tie a small stone at one end. Hold the
the earth. We know that all the planets go other end of the thread and whirl it
around the Sun. The moon goes around the round, as shown in Fig. 10.1.
earth. In all these cases, there must be some • Note the motion of the stone.
force acting on the objects, the planets and • Release the thread.
on the moon. Isaac Newton could grasp that • Again, note the direction of motion of
the same force is responsible for all these. the stone.
This force is called the gravitational force.
In this chapter we shall learn about
gravitation and the universal law of
gravitation. We shall discuss the motion of
objects under the influence of gravitational
force on the earth. We shall study how the
weight of a body varies from place to place.
We shall also discuss the conditions for
objects to float in liquids.
10.1 Gravitation
We know that the moon goes around the
earth. An object when thrown upwards,
reaches a certain height and then falls
downwards. It is said that when Newton was
sitting under a tree, an apple fell on him. The Fig. 10.1: A stone describing a circular path with a
velocity of constant magnitude.
fall of the apple made Newton start thinking.
He thought that: if the earth can attract an
apple, can it not attract the moon? Is the force Before the thread is released, the stone
the same in both cases? He conjectured that moves in a circular path with a certain speed
the same type of force is responsible in both and changes direction at every point. The
the cases. He argued that at each point of its change in direction involves change in velocity
orbit, the moon falls towards the earth, or acceleration. The force that causes this
instead of going off in a straight line. So, it acceleration and keeps the body moving along
must be attracted by the earth. But we do the circular path is acting towards the centre.
not really see the moon falling towards the This force is called the centripetal (meaning
earth. ‘centre-seeking’) force. In the absence of this
2020-21
, force, the stone flies off along a straight line. 10.1.1 UNIVERSAL LAW OF GRAVITATION
This straight line will be a tangent to the
circular path. Every object in the universe attracts every
other object with a force which is proportional
to the product of their masses and inversely
Tangent to a circle
proportional to the square of the distance
between them. The force is along the line
joining the centres of two objects.
More to know
A straight line that meets the circle
at one and only one point is called a Mm
F = G 2
tangent to the circle. Straight line d
ABC is a tangent to the circle at
point B.
Fig. 10.2: The gravitational force between two
uniform objects is directed along the line
The motion of the moon around the earth joining their centres.
is due to the centripetal force. The centripetal
force is provided by the force of attraction of Let two objects A and B of masses M and
the earth. If there were no such force, the m lie at a distance d from each other as shown
moon would pursue a uniform straight line in Fig. 10.2. Let the force of attraction between
motion. two objects be F. According to the universal
It is seen that a falling apple is attracted law of gravitation, the force between two
towards the earth. Does the apple attract the objects is directly proportional to the product
earth? If so, we do not see the earth moving of their masses. That is,
towards an apple. Why? F∝M × m (10.1)
According to the third law of motion, the And the force between two objects is inversely
apple does attract the earth. But according proportional to the square of the distance
to the second law of motion, for a given force, between them, that is,
acceleration is inversely proportional to the
mass of an object [Eq. (9.4)]. The mass of an 1
apple is negligibly small compared to that of F∝ (10.2)
d2
the earth. So, we do not see the earth moving
towards the apple. Extend the same argument Combining Eqs. (10.1) and (10.2), we get
for why the earth does not move towards the
moon. M ×m
In our solar system, all the planets go F ∝ (10.3)
d2
around the Sun. By arguing the same way,
we can say that there exists a force between M×m
the Sun and the planets. From the above facts or, F = G 2 (10.4)
d
Newton concluded that not only does the
earth attract an apple and the moon, but all where G is the constant of proportionality and
objects in the universe attract each other. This is called the universal gravitation constant.
force of attraction between objects is called By multiplying crosswise, Eq. (10.4) gives
the gravitational force. F×d2=GM×m
132 SCIENCE
2020-21
