PHYSICS

Chapter 10: Gravitation

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Gravitation
• According to Newton, every object in this Universe attracts every other object with
a certain force. This force with which two objects attract each other is called
gravitational force.
• If the masses of two bodies are small, then the gravitational force between them is very
small.
• The gravitational force holds the Solar System together.
• In our dairy life we have noticed things falling freely downwards towards earth when
thrown upwards or dropped from some height.
• Fact that all bodies irrespective of their masses are accelerated towards the earth with a
constant acceleration was first recognized by Galileo (1564-1642).
• The motion of celestial bodies such as moon, earth, planets etc. and attraction of moon
towards earth and earth towards sun is an interesting subject of study since long time.
• Toss a stone from a great height. What are your observations?
• The stone, which was at first at rest, begins to move towards the ground and reaches its
maximum speed right before it meets it.
• The stone is not travelling at a constant rate. Its speed fluctuates at all times, indicating
that the stone is accelerating.
• A force is necessary to cause an acceleration in a body, according to Newton's second law
of motion.
• The stone was not pushed or pulled in any way. What was the source of the force?
• Sir Isaac Newton came up with the solution to this dilemma after seeing an apple fall from
a tree.
• His thesis was that the apple is attracted to the Earth, and the Earth is attracted to the
apple The Earth's force on the apple is enormous, and as a result, the apple arrives on
Earth.
• The apple, on the other hand, is unable to draw the Earth since the force it exerts on it is
insignificant.
• As a result, we can deduce that the acceleration caused by Earth's immense force of
attraction is the cause of the stone's acceleration.
• It is evident from the preceding example that this force of attraction ties our complicated
universe together, keeps the moon revolving around the Earth, keeps all of the planets in
their orbits around the Sun, and helps us walk correctly on the Earth's surface.
• The force of gravitation, or gravitation, is a form of attraction that exists between any two
objects in the universe.
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• The force of gravity or gravity is the attraction or gravitational force between Earth (or
any planet) and any other material objects in the cosmos.

More About Gravitation

• You must have observed that whenever you throw any object upwards it reaches a
certain height and then falls downward towards the Earth. So, these objects are acting
under the gravitational pull of the Earth or gravitational forces which are forces of
attraction.
• Gravitational force or gravity of earth is responsible for pulling you and keeping you on
earth.
• Now each and every object in this universe that has mass exerts a gravitational force on
every other mass and the size of that pull depends on how large or small are the masses
of two objects under consideration.
• So for smaller masses like two human beings the gravitational force of attraction is very
small and is negligible because two peoples are not very massive
• Now when you consider massive objects like planets, Sun, Earth, Moon or other celestial
bodies, the gravitational pull becomes very strong.
• So here you must note that gravitational force depends on how massive objects under
consideration are.
• Gravity is very important on earth. It is the gravitational pull of earth that keeps our
planet orbiting round Sun.
• The motion of moon is also affected by both Sun and Earth.
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Why don't Moon Fall down

The moon revolves around the Earth due to centripetal force, which is the force of gravity
of the Earth. If the force of attraction between the Earth and moon ceases, then the moon
will continue to travel in a straight-line path tangential to its orbit around the Earth.
Centripetal force
When a body undergoes circular motion, it experiences a force that acts towards the center
of the circle. This center-seeking force is called a centripetal force.
• You must wonder If gravitational force is a force of attraction, then why does moon not
fall into earth?
• To understand this consider a person whirling a stone tied to a thread along a circular
path as shown below in the figure.
When an object is under free fall, acceleration due to gravity is constant at g = 9.8𝑚𝑠 −2
Value of g does not depend on mass i.e any object big or small experiences the same
acceleration due to gravity under free fall. All three equations of motion are valid for freely
falling objects as it is under uniform motion.
The sign of convention → towards earth g is +ve / away from earth g is -ve.
Weight and Mass
Mass of an object is the measure of its inertia and is constant throughout the universe.
Weight of an object keeps changing as the value of g changes. Weight is nothing but a force
of attraction of the Earth on an object = mg.
1
Weight of an object on the Moon is 6
times the weight on Earth.
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Thrust and Pressure

Force acting on an object perpendicular to the surface is called thrust. Effect of thrust
depends on the area of contact. The pressure is thrust per unit area. SI unit is the pascal (Pa).
Force acting on a smaller area applies more pressure than the same force acting on a larger
area.

• If he releases the stone then it flies along the tangent, at that point on the circular path.
• Before the release of thread, it is centripetal force responsible for the motion of stone in
the circular path where the stone moves with a certain speed and changes direction at
every point.
• During this motion the change in direction involves change in velocity which produces
acceleration. This force, which is called centripetal force, causes this acceleration, and
keeps the body moving along the circular path is acting towards the center.
• Now when the thread is released the stone does not experience this force and flies off
along a straight line that is tangent to the circular path.
• The motion of the moon around the earth is due to the centripetal force. The centripetal
force is provided by the force of attraction of the earth. If there were no such force, the
moon would pursue a uniform straight-line motion.
Pressure in fluids
The pressure exerted by a fluid in a container is transmitted undiminished in all directions on
the walls of the container.
Archimedes’ Principle – Why objects float or sink
The upward force exerted by a fluid on an object is known as upthrust or buoyant force.
The magnitude of buoyancy depends on the density of the fluid. If the density of an object is
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less than the fluid, it will float. If the density of the object is greater than the fluid, it will sink.

According to the Archimedes’ principle, when a body is immersed fully or partially in a fluid,
it experiences an upward force that is equal to the weight of the fluid displaced by it.
Relative Density
Relative density = Density of a substance/ Density of water
Elementary Idea Of Relative Density
In this article, we will understand what is relative density, calculations related to the relative
density, and density of various substances. Let us start with the definition of density.
What is Density?
Density is the amount of mass in a unit volume of matter, every substance has a different
density, to understand the idea of density let’s conduct an experiment, we will need a tall
glass cup, honey, water, coconut oil, and food coloring,
Step1: Pour a one-quarter cup of honey,
Step2: Pour a one-quarter cup of colored water gently on top of the honey.
Step3: pour a one-quarter cup of coconut oil on top of the colored water.

Notice how the different liquids from different layers, why is it so? The different substance
has a different density, which means for the same volume different substances weigh
differently, as they weigh differently heavier substances tend to settle at the bottom, like
honey and lighter material like oil tend to float at the top which means.
What is Relative Density?
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The difference between the specific gravity and density is that at room temperature and
pressure is 1gram per 1 cubic cm is the density of water this density is treated as a standard
and the density of any other material (usual liquids) is calculated relative to this is called
relative density or specific gravity.
Hence, specific gravity is the ratio of the mass of a substance to that of a reference
substance, let’s consider the density of honey is approx. 1.42 grams/cm3, so its specific
gravity would be 1.42/1 = 1.42. Notice that specific gravity is a ratio, therefore specific
gravity does not have a unit, and hence specific gravity is a dimensionless physical quantity.
The specific gravity of a substance will let us know if it will float or sink, it gives us the idea
about relative mass or relative density. If the specific gravity of a substance is below 1 then it
will float and if it is greater than 1 it will sink.
Let’s extend our experiment further for more liquids, this time, we will use several liquids
with different specific gravities, use the table given below for reference.

Material Density(gram/cm3)

Rubbing Alcohol 0.79

Lamp Oil 0.8

Baby Oil 0.83

Water 1.0

Milk 1.03

Liquid Soap 1.06

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Corn Syrup 1.33

Maple Syrup 1.37

Honey 1.42

Universal Law of Gravitation

Every object in the Universe attracts every other object with a force which is
proportional to the product of their masses and inversely proportional to the
square of the distance between them.

• This law was given by Sir Isaac Newton.

• Consider two objects A and B of mass ‘M’ and ‘m’ separated by a distance ‘r’.

• According to Newton’s law of gravitation, the force of attraction (F) between the two
objects is given as
GMm
F=
r2
where G is the proportionality constant known as the universal gravitation constant.
• Universal gravitation constant ‘G’ is numerically equal to the gravitational force of
attraction between the two bodies, each of unit mass kept at unit distance from
each other.
• The value of G is 6.67 × 10−11 Nm2/kg2.
• The universal law of gravitation successfully explained several phenomena such as
the motion of the Moon around the Earth, the motion of the planets around the
Sun and the force which binds us to the Earth.
Kepler’s Laws of Planetary Motion
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Kepler’s First Law

Kepler’s Second Law

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Kepler’s Third Law

Free Fall
• Whenever objects fall towards the Earth under the influence of gravitational force alone,
the objects are said to be in a state of free fall.
• The uniform acceleration produced in a freely falling body because of the
gravitational force of the Earth is known as acceleration due to gravity. It is
denoted by g, and its value on the surface of the Earth is 9.8 m/s2.
• During free fall, there is no change in the direction of motion of the object, but the
magnitude of the velocity of the falling object changes.
• The relation connecting the acceleration due to gravity g and universal gravitational
constant G is
GM
g=
R2
where M is the mass of the Earth and R is the radius of the Earth.
• The value of ‘g’ is maximum at the poles (where R is minimum) and minimum at the
equator (where R is maximum).
• The value of ‘g’ is maximum on the surface of the Earth; it decreases as we move
above or go beneath the surface of the Earth.
Motion of Objects under the Influence of Gravitational
Force of the Earth

• The equations of motion for freely falling bodies are

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where ‘u’ is the initial velocity, ‘v’ is the final velocity after ‘t’ sec and ‘h’ is the
height covered in ‘t’ sec.
• Here, g should be positive if the acceleration due to gravity is in the direction of
motion, and it should be negative if it is in the direction opposite to the motion.
Mass and Weight

• Mass of an object is the measure of its inertia.

• The force with which an object is attracted towards the Earth is the weight (W) of
the object. It is equal to the product of mass (m) and acceleration due to gravity (g).
W = mg
• SI unit of weight is Newton, same as that of force.
• The weight of an object on the Moon is one-sixth its weight on the Earth.
Differences between Mass and Weight

Mass Weight
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1. Mass of a body is the quantity of 1. Weight of a body is the force with

matter contained in it. which the body is attracted towards
the centre of the Earth.

2. Mass of a body is a constant 2. Weight of a body varies from place

quantity. to place.

3. It is a scalar quantity. 3. It is a vector quantity.

4. SI unit of mass is kilogram (kg). 4. SI unit of weight is newton (N).

Thrust and Pressure

• Thrust is the force acting perpendicularly on an object.
• Pressure is the force acting perpendicularly on a unit area of the object.

• SI unit of thrust is newton (N) and that of pressure is pascal (Pa), where 1 Pa = 1 N/m2
Density
• Density (d) of a substance is defined as mass (M) per unit volume (V).
M
d=
V

• The relative density of a substance is the ratio of its density to the density of water at 4°C.
Density of a substance
Relative density =
Density of water at 4oC

• Relative density has no units as it is the ratio of similar quantities.

Pressure in Fluids

• A fluid exerts pressure in all directions, even upwards.

• According to Pascal's law, pressure exerted in any confined mass of fluid is
transmitted uniformly in all directions.
Buoyancy
• When an object is partially or wholly immersed in a fluid, an upward force acts on
it, which is called upthrust or buoyant force.
• The magnitude of buoyant force depends on
✓ The volume of the object immersed in the liquid.
✓ The density of the liquid.
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• Let W be the weight of a body and FB be the buoyant force acting on it.
✓ If W > FB, then the body sinks.
✓ If W < FB, then the body floats.
• An object with density less than the liquid floats on the liquid. If the object is
denser than the liquid, then it sinks in the liquid.
Archimedes’ Principle

When an object is immersed wholly or partially in a fluid, it experiences an upward force

which is equal to the weight of the fluid displaced by it.

• The buoyant force acting on an object = Weight of fluid displaced by that object
Applications of Archimedes’ Principle
• In designing ships and submarines
• In determining the purity of milk with a lactometer
• In determining the density of liquids with a hydrometer
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Important Question
➢ Multiple Choice Questions:
1. Two objects of different masses falling freely near the surface of the moon would
(a) have same velocities at any instant
(b) have different acceleration
(c) experience forces of same magnitude
(d) undergo a change in their inertia
2. The value of acceleration due to gravity
(a) is same on equator and poles
(b) is least on poles
(c) is least on equator
(d) increases from pole to equator
3. The gravitational force between two objects is F. If masses of both objects are halved
without changing the distance between them, then the gravitational force would
become
(a) F/4
(b) F/2
(c) F
(d) 2F
4. A boy is whirling a stone tied to a string in a horizontal circular path. If the string
breaks, the stone
(a) will continue to move in the circular path
(b) will move along a straight line towards the centre of the circular path
(c) will move along a straight line tangential to the circular path
(d) will move along a straight line perpendicular to the circular path away from the boy
5. An object is put one by one in three liquids having different densities. The object
1 2 3
floats with , and parts of their volumes outside the liquid surface in liquids of
9 11 7
densities d1, d2 and d3 respectively. Which of the following statement is correct?
(a) d1 > d2 > d3
(b) d1 > d2 < d3
(c) d1 < d2 > d3
(d) d1 < d2 < d3
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6. In the relation F = GM mld2, the quantity G

(a) depends on the value of g at the place of observation
(b) is used only when the Earth is one of the two masses
(c) is greatest at the surface of the Earth
(d) is universal constant of nature
7. Law of gravitation gives the gravitational force between
(a) the Earth and a point mass only
(b) the Earth and Sun only
(c) any two bodies having some mass
(d) two charged bodies only
8. The value of quantity G in the law of gravitation
(a) depends on mass of Earth only
(b) depends on radius of Earth only
(c) depends on both mass and radius of Earth
(d) is independent of mass and radius of the Earth
9. Two particles are placed at some distance. If the mass of each of the two particles is
doubled, keeping the distance between them unchanged, the value of gravitational
force between them will be
1
(a) times
4
(b) 4 times
1
(c) times
2
(d) unchanged
10. The atmosphere is held to the Earth by
(a) gravity
(b) wind
(c) clouds
(d) Earth’s magnetic field
➢ Very Short Question:
1. What is the S.I. unit of thrust?
2. What is the S.I. unit of pressure?
3. Define thrust.
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4. Define pressure.
5. Why is it easier to swim in sea water than in river water?
6. Why a truck or a motorbike has much wider tires?
7. Why are knives sharp?
8. Why is the wall of dam reservoir thicker at the bottom?
9. Why do nails have pointed tips?
10. While swimming why do we feel light?
➢ Short Questions:
1. State the difference in balanced and unbalanced force.
2. What change will force bring in a body?
3. When a motorcar makes a sharp turn at a high speed, we tend to get thrown to one
side. Explain why?
4. Explain why it is dangerous to jump out of a moving bus.
5. Why do fielders pull their hand gradually with the moving ball while holding a
catch?
6. In a high jump athletic event, why are athletes made to fall either on a cushioned
bed or on a sand bed?
7. How does a karate player breaks a slab of ice with a single blow?
8. What is law of conservation of momentum?
➢ Long Questions:
1. With the help of an activity prove that the force acting on a smaller area exerts a
larger pressure?
➢ Assertion Reason Questions:
1. For two statements are given- one labelled Assertion (A) and the other labelled
Reason (R). Select the correct answer to these questions from the codes (a), (b), (c)
and (d) as given below:
a. Both Assertion and Reason are correct, and reason is the correct explanation for
assertion.
b. Both Assertion and Reason are correct, and Reason is not the correct explanation
for Assertion.
c. Assertion is true but Reason is false.
d. Both Assertion and Reason are false.
Assertion: Universal gravitational constant G is a scalar quantity.
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Reason: The value of G is same through out the universe.

2. For two statements are given- one labelled Assertion (A) and the other labelled
Reason (R). Select the correct answer to these questions from the codes (a), (b), (c)
and (d) as given below:
a. Both Assertion and Reason are correct, and reason is the correct explanation for
assertion.
b. Both Assertion and Reason are correct, and Reason is not the correct explanation
for Assertion.
c. Assertion is true but Reason is false.
d. Both Assertion and Reason are false.
Assertion: When distance between two bodies is doubled and also mass of each
body is doubled, then the gravitational force between them remains the same.
Reason: According to Newton’s law of gravitation, product of force is directly
proportional to the product mass of bodies and inversely proportional to square of
the distance between them.
➢ Case Study Questions:
1. Every object in the universe attracts every other object with a force which is
proportional to the product of their masses (m1*m2) and inversely proportional to the
square of the distance (d2) between them. The force is along the line joining the centers
of two objects.

(i) Gravitational force does not depend on

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(a) Masses of objects

(b) Separation between objects
(c) Charges on objects
(d) None of these
(ii) Force of gravitation varies with masses of object as:
(a) Product of masses
(b) Sum of masses
(c) Difference of masses
(d) None of these
(iii) When mass of one body is doubled then force of gravitation will become:
(a) Force will remain same
(b) Force will become double
(c) Force will become halved
(d) None of these
(iv)What is universal gravitational constant? What is its SI unit?
(v) Two objects of masses 10kg and 20kg separated by distance 10m. What is
gravitational force between them?
2. We know that the earth attracts every object with a certain force and this force
depends on the mass (m) of the object and the acceleration due to the gravity (g). The
weight of an object is the force with which it is attracted towards the earth.
Mathematically
W=mxg
Where, W= weight of object
m= mass of object
g= acceleration due to the gravitational force
As the weight of an object is the force with which it is attracted towards the earth, the
SI unit of weight is the same as that of force, that is, Newton (N). The weight is a force
acting vertically downwards; it has both magnitude and direction. We have learnt that
the value of g is constant at a given place. Therefore at a given place, the weight of an
object is directly proportional to the mass, say m, of the object, that is, W αm. It is due
to this reason that at a given place, we can use the weight of an object as a measure of
its mass. Answer the following questions.
(i) Unit of acceleration due to the gravity (g) is:
(a) m/s
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(b) m/s2
(c) Newton(N)
(d) None of these
(ii) Direction of weight of any object is:
(a) Always towards centre of earth
(b) Always away from centre of earth
(c) Weight don’t have direction
(d) None of these
(iii) Which of the following has same unit:
(a) Mass and weight
(b) Weight and force
(c) Velocity and acceleration
(d) None of these
(iv) Whether weight is scalar quantity or vector quantity? Justify your answer.
(v) Differentiate between mass and weight.