1. The document discusses concepts related to gravitation including the motion of the moon around Earth, centripetal force, Kepler's laws of planetary motion, Newton's law of universal gravitation, and Archimedes' principle. 2. Key points covered include that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. 3. Archimedes' principle states that the upward buoyant force on an object immersed in a fluid is equal to the weight of fluid displaced by the object.

1. Chapter-10
Gravitation
Prepared By
N.Aarthi B.E, M.Tech
SASTRA

2. Motion of Moon around Earth

3. • Moon goes around the earth.
• Object thrown upwards reaches certain height
and then falls downwards.
• If earth can attract apple in Newton's case,
can it not attract moon?

4. Activity to understand motion of moon

5. • Before thread is released stone moves in a
circular path with certain speed and changes
direction at every point.
• Change in direction involves change in velocity
or acceleration.
• Force that causes acceleration and keeps
body moving is acting towards centre.
• This force is called Centripetal force.
• In absence of this force, the stone flies off
along a straight line which is tangent to
circular path.

6. Straight line that meets the circle at
one and only one point is called
tangent to the circle

7. Does the apple attract the earth?
• According to 3rd law of motion, apple
does attract the earth.
• But as per 2nd law, for a given force,
acceleration is inversely proportional to
the mass of object.
• Mass of apple is negligibly small
compared to mass of earth.
• So we do not see earth moving towards
apple.

8. Solar System

9. • In our solar system, all planets go around
sun.
• There exists force between sun and the
planets.
• Newton concluded that not only does
earth attract the apple and moon, but all
objects in universe attract each other.
• This force of attraction between objects
is called the gravitational force.

10. Gravitation Vs Gravity

12. Universal Law of Gravitation
Value of G = 6.673∗10−11Nm2Kg−2

13. • According to universal law of gravitation, force
between 2 objects is directly proportional to
the product of their masses.
• And inversely proportional to their square of
the distance between them.

15. Value of G=6.673*10 -11

16. Johannes Kepler laws of planetory motion

17. Kepler First law – The Law of Orbits
• All the planets revolve around the sun in
elliptical orbits having the sun at one of the
foci.
• The point at which the planet is close to the
sun is known as perihelion and the point at
which the planet is farther from the sun is
known as aphelion.
• It is the characteristics of an ellipse that the
sum of the distances of any planet from two
foci is constant. The elliptical orbit of a planet
is responsible for the occurrence of seasons.

19. Kepler’s Second Law – The Law of Equal
Areas
The radius vector drawn from the sun to the
planet sweeps out equal areas in equal intervals
of time.

21. Kepler’s Third Law – The Law of Periods
• The square of the time period of revolution of
a planet around the sun in an elliptical orbit is
directly proportional to the cube of its semi-
major axis”.
• T2 α r3
• R3 / T2 = Constant
• Shorter the orbit of the planet around the sun,
shorter the time taken to complete one
revolution

23. Newton's Inverse Square law
Newton used kepler’s 3rd law to calculate
gravitational force of attraction.
Orbital velocity is v, Radius of orbit is r
Force acting on orbiting planet is given by
F α v2/r
If T denotes period, then v=distance/time
v= 2 πr/T
So that v2 = (2 πr/T)2
V2=4 π2r2/T2

24. But we know that T2 α r3
V2=4 π2r2/r3
V2 α 1/r
But we know that F α v2/r
Therefore F α 1/r2
Note:
If distance gets bigger by factor of 6 then F
becomes 1/36 times smaller.

27. Importance of Universal law of
Gravitation
• It binds us to the earth.
• It is responsible for the motion of the moon
around the earth.
• It is responsible for the motion of planets
around the Sun.
• Gravitational force of moon causes tides in
seas on earth.

30. Free Fall
• Freefall is defined as a situation when a body is
moving only under the influence of the earth’s
gravity.
• Since external force is acting on the ball, the
motion will be accelerated.
• This free-fall acceleration is also known
as acceleration due to gravity.
• Let us find the value acceleration due to gravity
during free fall.
• To find this, we take one assumption that the
height from which the ball is dropped is very
small as compared to the radius of the earth.

31. Free fall

32. Free Fall

34. • From equation (3) we can see that g depends
on the dimension of the body i.e. mass and
radius. Hence, it will not be the same
everywhere.
• Also, as the acceleration remains constant
during free-fall motion, so we can use
equations of motion.
• We just have to replace the value of
acceleration in all the equations with g.
• For example, v = u + gt

35. To calculate value of g

40. Mass- Mass of an object is the measure of
its inertia and is constant throughout the
universe

41. Weight
• 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
• Weight of an object on the Moon
is 1/6 times the weight on Earth.
• It is the measure of the force of gravity
acting on a body.
• The formula for weight is given by:
w = mg

42. • It depends on mass and the acceleration due to
gravity, the mass may not change but the
acceleration due to gravity does change from
place to place.
Example
Shape of the earth is not completely spherical, but
an oblate spheroid, therefore a person standing at
the equator is far away from the center of the earth
than a person standing at the north pole, as
acceleration due to gravity is proportional to the
inverse of the square of the distance between two
objects, a person standing at the north pole would
experience more weight as he is closer to the
center of the earth than a person standing at the
equator.

43. What is the Difference between Mass and
Weight?

44. Astronauts feel Weightlessness?

45. • The space stations are orbiting the earth it is
actually falling towards the earth indefinitely
and everything in it is falling including the
astronauts so the astronauts experience
weightlessness and can float freely around.
• Weight can increase or decrease depending
on the acceleration due to gravity but the
mass remains unchanged.

46. Weight of an object on the moon

48. 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.

49. Pressure
Pressure is defined as the
force per unit area. If a force F
is applied on a surface of area
A, then the pressure P is
defined as:
P = F/A
Pressure is expressed in N/m2 which is
also called a Pascal (Pa).

55. Pressure in fluids-Example

57. Pressure in fluids
• All liquids and gases are fluids
• Fluids have weight and they also exert
pressure on base and walls of the
container.
• Pressure is transmitted undiminished in
all directions.

58. Buoyancy
We can define Buoyancy as:
• The upward force applied by the fluid on the
object or the body when an object is put in or
submerged in the fluid.
• The unit of the buoyant force is the Newton
(N).

59. • When a body is in water, it displaces some
amount of water owing to its weight.
• The amount of displaced water is computed by
the object’s density which relates to volume.
• The volume of a cricket ball and beach ball can be
the same as their different weight their density
differs.
• The solid steel block descends in water but the
steel ship does not. Therefore, the quantity of
displaced water in the upward direction is
elucidated in terms of Buoyant force.

60. Buoyancy

61. Buoyancy

63. • We can say, when immersed in water or any
other fluid, the body experiences a force from
the downward direction opposite to the
direction of the gravitational pull, which is
responsible for the decrease in its weight.
• It can be the reason why a ball of plastic
floats in water rather than sinking to the base
by its weight.
• But here too, we observe that some objects
such as a plastic bottle float over water, while
others such as a needle sink.

64. Why objects float or sink?

65. • The cork floats while nail sinks.
• Density of substance is defined as mass per
volume.
• Density of cork is less than density of water.
• Upthrust of water on cork is greater than the
weight of cork. So it floats.
• Density of iron nail is more than density of
water.
• Upthrust of water on iron nail is less than
weight of iron nail. So it sinks.

66. Objects that Sink/float

67. Archimede’s Principle
The upward buoyant force that is exerted
on a body immersed in a fluid, whether
partially or fully submerged, is equal to
the weight of the fluid that the body
displaces and acts in the upward direction
at the center of mass of the displaced
fluid

68. • The value of thrust force is given by the
Archimedes law which was discovered by
Archimedes of Syracuse of Greece.
• When an object is partially or fully immersed in a
liquid, the apparent loss of weight is equal to the
weight of the liquid displaced by it.
• Because the actual gravitational force is
decreased by the liquid’s upthrust, the object
feels as though its weight is reduced. The
apparent weight is thus given by:
• Apparent weight= Weight of object (in the air) –
Thrust force (buoyancy)

69. • Archimedes’s principle tells us that this loss of
weight is equal to the weight of liquid the
object displaces.
• If the object has a volume of V, then it
displaces a volume V of the liquid when it is
fully submerged.
• If only a part of the volume is submerged, the
object can only displace that much of liquid.

70. Archimedes Principle Formula
Fb = ρ x g x V
Where,
Fb is the buoyant force
ρ is the density the fluid
V is the submerged volume
g is the acceleration due to gravity

71. Archimedes Principle Experiment

72. • Take a mug filled with water to the brim and
place it in an empty bowl.
• Now take any solid object you like and measure
its weight using a spring balance. Note this down.
• Keep the object attached to the spring balance
and submerge it in the water. Just make sure the
spring balance is not submerged.
• Now, note down the weight shown by the spring
balance. You will notice that it is less. Some water
will be displaced into the bowl.
• Collect this water and weigh it. You will find that
the weight of the water will be exactly equal to
the loss of weight of the object!

73. Archimedes Principle Derivation

74. Archimedes Principle in Daily life

75. Archimedes Principle in Daily life

76. The reason why submarines are always underwater is that
they have a component called ballast tank which allows
the water to enter making the submarine be in its position
underwater as the weight of the submarine is greater than
the buoyant force.

77. The reason why hot-air balloons rise and
float in mid-air is because the buoyant
force of the hot-air balloon is less than the
surrounding air. When the buoyant force
of the hot-air balloon is more, it starts to
descend. This is done by varying the
quantity of hot air in the balloon.

78. A hydrometer is an instrument used for
measuring the relative density of liquids.
Hydrometer consists of lead shots which
makes them float vertically on the liquid. The
lower the hydrometer sinks, the lesser is the
density of the liquid.

81. Relative density
• The density of substance is defined as mass of
a unit volume.
• Unit of density is kilogram per metre cube.
• Density of gold is 19300 kg/m3 while that of
water is 1000kg/m3
• Density helps to determine its purity.
• Relative density= Density of a substance
Density of water
• It has no unit.

83. MCQ
1. Even though stone also attracts earth
towards itself, earth does not move
(a) Because of greater mass of earth
(b) Because of lesser mass of stone
(c) Force exerted by stone is less
(d) Force exerted earth is large
Ans. (a) Because of greater mass of earth

84. 2. Weight of an object has S.I, unit of:
(a) Newton
(b) Kg
(c) N/Kg
(d) Kg/N
Ans. (a) Newton
3. Which of the statements is correct?
(a) Mass is constant and weight is variable
(b) Mass is variable and weight is constant.
(c) Both Mass and weight are variable
(d) Both Mass and weight are constant.
Ans. (a) Mass is constant and weight is variable

85. 4. If cross – sectional area of an object is more
than the pressure applied by the external force
is: (a) Less (b) More (c) Remains same (d) None
of the above.
Ans. (a) Less
5. If the acceleration due to gravity at a place is
more, the weight of that object will: (a)
Decrease (b) Increase (c) Remains same
(d) None of the above
Ans. (b) Increase

86. 6. Weight of the object is:
(a) More at the equator and less at poles (b)
More at poles and less at equator (d) Same at
poles and equator (d) Depend on Mass of the
object
Ans. (b) More at poles and less at equator
7. If the distance between the object increase,
mass remaining same then the gravitational
forces between the object will :-
(a) Increase (b) Decrease (c) Remain same (d)
None of the above.
Ans. (a) Increase

87. 8. The S. I. units of mass, force and weight are
respectively:
(a) Kg, N, N (b) N, Kg, N (c) N, N, Kg (d) Kg, N, Kg
Ans. (a) Kg, N, N
9. Gravitational force acts on all objects in
proportion to their masses. Why then, a heavy
object does not fall faster than alight object?
Ans. In free fall of objects the acceleration in
velocity due to gravity is independent of mass of
those objects hence a heavy object does not fall
faster than alight object.

88. THANK YOU
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