2. Contents:
1. Introduction to Gravitation.
2. Centripetal force
3. Universal Law of Gravitation
4. Importance Of the Universal law of Gravitation
5. Free fall
6. To calculate the value of “g”
7. Mass and Weight
8. Weight of an object on the moon
9. Thrust and pressure
10.Pressure in fluids
11.Buoyancy
12.Why objects float or sink when placed on the surface of water
13.Archimedes’ Principle
14.Relative density
3. 1.Introduction to Gravitation
Earth attracts everything towards it by an unseen force of attraction.
This force of attraction is known as gravitation or gravitational pull.
And
“Gravitation is the force of attraction between the two object in the
universe”
a)Gravitation may be the attraction of objects by the
earth.
Eg :- i) If a body is dropped from a certain height, it falls
downwards due to earth's gravity.
ii)If a body is thrown upwards, it reaches a certain
height and then falls downwards due to the
earth's gravity.
b)Gravitation may be the attraction between objects in
outer space.
Eg :- Attraction between the earth and moon.
Attraction between the sun and planets.
6. 2.Centripetal force :-
When a body moves ina circular path, it changes its direction at every
point.The force which keeps the body in the circular pathacts towards the
centre of the circle. This force is called centripetal force.
If there is no centripetalforce, the bodywillmove inastraightline tangentto
thecircular path.
Hence
Example
Force Towards the
Centre
7. 3.Universal Law of Gravitation:
Every object in the universe attracts other object by a force of attraction,
called gravitation, which is
i) directly proportional to the product of masses of the objects and
ii) inversely proportional to the square of distance between them.
This is called Law of Gravitation or Universal Law of Gravitation.
Let masses (M) and (m) of two objects A and B are distance (d) apart.
Let F be the attractional force between two masses.
A B
Using equation 1
𝐹𝑋𝑑2 = 𝐺𝑀𝑋𝑚
𝐺 =
𝐹𝑑2
𝑀𝑋𝑚
And SI Unit of G 𝑁𝑚2
𝑘𝑔−2
or 𝑁𝑚2
/𝑘𝑔2
F
a
b
From a and b
1
8. Note: When the value of one quantity increases with respect to decrease in other
or vice-versa, then they are said to be inversely proportional.
It means that the two quantities behave opposite in nature.
9. 5.Importance Of the Universal law of Gravitation:
•the force 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.
What Causes Tides?
1. Tides are caused by the
Interaction of earth, the moon,
and the sun.
2. Gravity is the reason for tides.
3. Gravity is the force exerted
by an object that pulls other
objects towards it.
4.The moon pulls water on the earth toward itself, causing a bulge on the side of
the earth near the moon
12. Sir Isaac Newton was an English
mathematician physicist who lived from
1642-1727.
The legend is that Newton discovered
Gravity when he saw a falling apple
while thinking about the forces of
nature.
Who discovered Gravity?
THERE IS A DIFFERENCE BEWEEN
GRAVITY AND GRAVITATION
i.e G and g
13. 6.Free Fall:
Throwing a
stone upwards
It reaches
a certain height
And then it
starts falling down
Why Its fall?
Its due to Gravitational force.
The Gravitational force F will be equal to the product of the mases and
acceleration due to the gravitational force, that is
F=M.g--------(1)
14. Acceleration Due to Gravity:
When an object falls towards the earth there is a change in its acceleration
due to the gravitational force of the earth. So this acceleration is
called acceleration due to gravity.
The acceleration due to gravity is denoted by g.
The unit of g is same as the unit of acceleration, i.e., ms−2
Mathematical Expression for g
From the second law of motion, force is the product of mass
and acceleration.
F = ma
For free fall, acceleration is replaced by acceleration due to gravity.
Therefore, force becomes:
F = mg ….(i)
But from Universal Law of Gravitation
15.
16. Steps to Calculate the value of g:
Difference between Gravitation
Constant (G) and Gravitational
Acceleration (g)
S.
No.
Gravitation
Constant (G)
Gravitational
acceleration (g)
1. Its value is 6.67×10-
11Nm2/kg2.
Its value is 9.8
m/s2.
2 Its unit is Nm2/kg2. Its unit is m/s2.
6.To Calculate the Value of “g”:
6.4X10 m
6
17. 7. Mass and Weight:
Mass:
The mass of a body is the measure of its inertia. If the mass of a body is
more its inertia is more.
The mass of a body is constant and does not change from place to place.
The SI unit of mass is “kg”.
Weight:
The weight of a body is the force with which the earth attracts the body.
The force with which a body is attracted by the earth depends on its mass m
and acceleration due to gravity g.
F = m x g
Since weight of a body is the force with which the earth attracts the body,
W = m x g
Since g at a place is constant.
The weight of a body changes from place to place.
The SI unit of weight is the same as force - Newton (N).
19. 8.Weight of an object on the moon:
The weight of an object on the earth is the force with which the earth attracts the
object.
In the same way, The weight of an object on the moon is the force with which the
Moon attracts that object.
The mass of the moon is less than that of the earth. Due to this the moon
exerts lesser force of attraction on objects.
Let the mass of an object be m
÷
22. 9. Thrust and Pressure:
Thrust :-
Thrust is the force acting on an object
perpendicular to the surface.
Eg :- When you stand on loose sand the force
(weight) of your body is acting on an area
equal to the area of your feet. When you lie
down, the same force acts on an area equal
to the contact area of the whole body. In
both cases the force acting on the sand
(thrust) is the same.
Therefore the effect of thrust
depends on the area on which it acts.
Pressure :-
Pressure is the force acting on unit area of
a surface.
Pressure =
𝑇ℎ𝑢𝑟𝑠𝑡
𝐴𝑟𝑒𝑎
The SI unit of thrust is N/𝑚2or N 𝑚−2
The Si unit of pressure is also called pascal,
Denoted as Pa.
23. Example-10.6:
A block of wood is kept on a tabletop. The
mass of wooden block is 5 kg and its
dimensions are 40 cm × 20 cm × 10 cm.
Find the pressure exerted by the wooden
block on the table top if it is made to lie on
the table top with its sides of dimensions
(a) 20 cm × 10 cm and (b) 40 cm × 20 cm.
Solution :
(a) The mass of the wooden block = 5 kg
The dimensions = 40 cm × 20 cm × 10 cm
Here, the weight of the wooden block applies
a thrust on the table top.
That is,
Thrust = F = m × g
= 5 kg × 9.8 m s–2
= 49 N
Area of a side = length × breadth
= 20 cm × 10 cm
= 200 cm2 = 0.02 m2
From Eq. (20),
Pressure= 49 N ⁄ 0.02m2
= 2450 N m-2.
(b) When the block lies on its side of
dimensions 40 cm × 20 cm, it exerts the
same thrust.
Area = length × breadth
= 40 cm × 20 cm
= 800 cm2 = 0.08 m2
From Eq. (20),
Pressure= 49 N ⁄ 0.08m2
= 612.5 N m–2
The pressure exerted by the side 20 cm× 10
cm is 2450 N m–2 and by the side 40 cm × 20
cm is 612.5N m–2.
24. 10. Pressure in a Fluids:
What Is a Fluid?
Substance that can flow from place to place, and take the shape of a container.
-- Liquids and gases are called fluids.
EX: Inks, Paint, glue,water.
All liquids and gases are fluids. A solid exerts pressure on a surface due to its
Weight. Similarly, Fluids have weight, and they also exerts pressure on the base
and walls of the container in which they are enclosed. Pressure exerted in any
confined mass of fluid is transmitted undiminished in all directions.
25. 11. Buoyancy (Upthrust):
When an object is immersed in a fluid it experiences an upward force called buoyant force. This
property is called buoyancy or upthrust.
The force of gravity pulls the object downward and the buoyant force pushes it upwards.
The magnitude of the buoyant force depends upon the density of the fluid.
26. 12. Why objects float or sink when placed on the surface of water?
If the density of an object is less than the density of a liquid, it will float on the
liquid and if the density of an object is more than the density of a liquid,
it will sink in the liquid.
Activity: Take some water in a beaker. Take a piece
of Pen cap and an iron nail of the same
mass. Place them on the water. The pen
cap floats and the nail sinks.
The pen cap floats because the density of
cap is less than the density of water and
the upthrust of water is more than the
weight of the cap.
The nail sinks because the density of the
iron nail is more than the density of water
and the upthrust of water is less than the
weight of the nail.
27. 13. Archimede’s Principle:
Archimedes' principle states that,' When a body is partially or fully
immersed in a fluid it experiences an upward force that is equal to the
weight of the fluid displaced by it.'
Archimedes principle has many uses.It is used in
designing ships and submarines, Hydrometers used
to determine the density of liquids,lactometers used
to determine purity of milk etc.
28. 13. Density and Relative density:
Density is a measure of mass per unit of volume.
Relative density: The relative density of a substances is the ratio of the substance
to the density of water.
